Regression analysis is one of the important tools to the researchers, except the complex, cumbersome and the expensive undertaking of it; especially in obtaining the estimates correctly and interpreting them plentifully. We perceive a need for more inclusive and thoughtful interpretation of (in this example) multiple regression results generated through SPSS. The objective of this study is to comprehend and demonstrate the in-depth interpretation of basic multiple regression outputs simulating an example from social science sector. In this paper we have mentioned the procedure (steps) to obtain multiple regression output via (SPSS Vs.20) and hence the detailed interpretation of the produced outputs has been demonstrated. We have illustrated the interpretation of the coefficient from the output, Model Summary table (R2, Adj. R2, and SE); Statistical significance of the model from ANOVA table, and the statistical significance of the independent variables from coefficients table. An expansive and attentive interpretation of multiple regression outputs has been explained untiringly. Both statistical and the substantive significance of the derived multiple regression model are explained. Every single care has been taken in the explanation of the results throughout the study to make it a competent template to the researcher for any real-life data they will use. Because every effort has been made to clearly interpret the basic multiple regression outputs from SPSS, any researcher should be eased and benefited in their fields when they use multiple regression for better prediction of their outcome variable.

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International Journal of Science and Research (IJSR)

ISSN: 2319-7064

ResearchGate Impact Factor (2018): 0.28 | SJIF (2018): 7.426

Volume 8 Issue 6, June 2019

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Licensed Under Creative Commons Attribution CC BY

Interpreting the Basic Outputs (SPSS) of Multiple

Linear Regression

Chuda Prasad Dhakal, PhD

Tribhuvan University, Institute of Agriculture and Animal Sciences, Rampur Campus, Chitwan, Nepal

Abstract: Regression analysis is one of the important tools to the researchers, except the complex, cumbersome and the expensive

undertaking of it; especially in obtaining the estimates correctly and interpreting them plentifully. We perceive a need for more inclusive

and thoughtful interpretation of (in this example) multiple regression results generated through SPSS. The objective of this study is to

comprehend and demonstrate the in-depth interpretation of basic multiple regression outputs simulating an example from social science

sector. In this paper we have mentioned the procedure (steps) to obtain multiple regression output via (SPSS Vs.20) and hence the

detailed interpretation of the produced outputs has been demonstrated. We have illustrated the interpretation of the coefficient from the

output, Model Summary table (R 2, Adj. R2, and SE); Statistical significance of the model from ANOVA table, and the statistical

significance of the independent variables from coefficients table. An expansive and attentive interpretation of multiple regression

outputs has been explained untiringly. Both statistical and the substantive significance of the derived multiple regression model are

explained. Every single care has been taken in the explanation of the results throughout the study to make it a competent template to the

researcher for any real-life data they will use. Because every effort has been made to clearly interpret the basic multiple regression

outputs from SPSS, any researcher should be eased and benefited in their fields when they use multiple regression for better prediction

of their outcome variable.

Keywords: Multiple regression,Regression outputs, R squared, Adj. R Square, Standard error, Multicollinearity

1. Introduction

Regression analysis technique is built on many statistical

concepts including sampling, probability, correlation,

distributions, central limit theorem, confidence intervals, z-

scores, t-scores, hypothesis testing and more (Interpreting

regression output, without all the statistics theory,

n.d).Interpretation of the results catches up the issues of 1)

analysing the correlation and directionality of the data, 2)

estimating the model, i.e., fitting the line, and 3) evaluating

the validity and usefulness of the model. Hence interpreting

its output generally is bulky. One example that suits this

issue (interpreting of the regression results) is, Nathans et

al.(2012) reveals that, there is no single right way to

interpret regression results, and although reliance on beta

weights may feel right because it is normative practice, it

provides very limited information. Also, the authors

[(Martin, 2018); (Klees, 2016); (Armstrong, 2011); (Dion,

2008); (Guthery & Bingham, 2007); (Seva et al., 2010) and

(Miler, n.d)]; have shed light on the importance and the

power of regression and its challenge if the models

investigated were valid at all.

To obtain credible and valid estimates of regression passing

across frequent cumbersome steps that may derail at any

time of the analysis, and interpreting them (the regression

results) is always a challenge. In their papers the authors

mentioned above have emphasized on, the caution any

researcher has to take, s/he has to seek to reach their correct

results and interpretation, about the completeness and the

comprehensive level of interpretation. The dimension the

interpretation has to cover for any balanced presentation of

the regression results (both statistical and the substantive

significance) when writing an application of the regression

(especially multiple regression) results.

Keeping this view, this paper is intended to be a quick a nd

easy-to -follow summary of the interpreting of regression

analysis outputs. However, the scope of this paper is limited

to shed light only on basic insights the regression output

gives, based on the multiple regression output that looks like

in SPSS software.

In this paper we want to open researchers‟ eyes wide

through which multiple regression output can be viewed

successfully. For instance, as Sweet and Karen (2012)

initiate the discussion as, „interpretation of the statistics in

multiple regression is, the same as in bivariate regression,

other than in multiple regression the effects of multiple

independent variables often overlap in their association with

the dependent variable.

This paper is structured by (a) defining data (b) considering

the specified no of basic multiple regression output (c)

describing how each output are interpreted, and (d)

summarizing the discussion. In conclusion, we will

demonstrate a data-driven example and a results and

discussion section that researchers can use as a template for

interpreting and reporting multiple regression outputs.

2. Materials and Methods

For twelve families, hypothetical data (Table 1): dependent

variable (y) = hours per week husband spends in house

work, and the two independent variables, x1 = no of children

in the families, x 2 = wife's years of educationand

x3 =husband‟s years of education, is considered for the study.

Table 1: Hypothesized data

Family A B C D E F G H I J K L

Y 4 1 3 5 3 2 4 5 4 4 4 5

x1 3 0 3 2 2 1 3 4 4 3 2 3

x2 16 10 14 18 14 14 12 14 16 12 16 16

x3 18 18 16 12 16 18 12 12 14 12 16 16

International Journal of Science and Research (IJSR)

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Volume 8 Issue 6, June 2019

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Any fit of a multiple regression model is valid, if and only if

satisfied are the underlying assumptions,1) dependent

variable should be measured on a continuous scale (i.e., it is

either an interval or ratio variable). 2) there are two or more

independent variables, which can be either continuous (i.e.,

an interval or ratio variable) or categorical (i.e., an ordinal or

nominal variable). 3) independence of observations

(i.e., independence of residuals), 4) linear relationship

between (a) the dependent variable and each of the

independent variables, and (b) the dependent variable and

the independent variables collectively. 5) homoscedasticity

6) data must not show multicollinearity, 7) there should

be no significant outliers, high leverage points or highly

influential points and 8) the residuals (errors) are

approximately normally distributed.

Considering none of the eight assumptions mentioned

earlier, have been violated, regression output to the given

data was generated through the following steps conducted in

SPSS Vs. 20.

Click„Analyse‟ , „Regression‟ , „Linear‟ . Select „hours per

week‟ in the dependent variable box and „no of children‟ and

„years of education‟ in the independent variable box. Select

„enter‟ as the as the method [The default method for the

multiple linear regression analysis]. Click „Statistics‟, select

[„Model fit‟ and „Estimates‟ are default selections] „R

squared change‟, „Confidence Intervals‟, „Part and partial

correlations‟ and „Collinearity diagnostics‟ and click

„continue‟. Outputs (Model summary table, Anova and

Coefficients) generated through the command mentioned

afore are discussed and interpreted systematically in the

following result and discussion section. At times while

discussing, same output table has been replicated as per the

ease to see the results close by.

3. Results and Discussion

Our research question for the multiple linear regression is:

Can we explain the outcome variable, hours per week that a

husband spends at house work with the given independent

variables no of children , wife's year of education and

husband's years of education?

Determining how well the model fits

The first table of interest is the model summary (Table 2).

This table provides the R , R2 , adjusted R2 , and the standard

error of the estimate, which can be used to determine how

well a regression model fits the data:

Table 2: Model summary

Model summary

Model R R Square Adjusted

R Square Std. Error of

the estimate

1 .925a .856 .803 .547

a. Predictors: (Constant), husband‟s years of education,

wife‟s years of education, no of children

The "R" column represents the value of R, the multiple

correlation coefficient. R can be considered to be one

measure of the quality of the prediction of the dependent

variable; in this case, hours per week. A value of .925 in this

example, indicates a good level of prediction. The "R

Square" column represents the R2 value (also called the

coefficient of determination), which is the proportion of

variance in the dependent variable that can be explained by

the independent variables.

You can see from our value of .856 that our independent

variables explain 85.6 % of the variability of our dependent

variable, hours per week. And 14.4% (100%-85.6%) of the

variation is caused by factors other than the predictors

included in this model. At first glance, R-squared seems like

an easy to understand statistic that indicates how well a

regression model fits a data set. However, it doesn‟t tell us

the entire story. To get the full picture, one must consider

R2 value in combination with residual plots, other statistics,

and in-depth knowledge of the subject area.

According to Frost (2017) caveats about R2 is: small R-

squared values are not always a problem, and high R-

squared values are not necessarily good. For instance, for an

outcome variable like human behaviour which is very hard

to predict, a high value of R-squared is almost impossible.

And, this does not mean any predicted model to such case is

always useless. A good model can have a low R2 value. On

the other hand, a biased model can have a high R2 value! A

variety of other circumstances can artificially inflate R 2 .

To accurately report the data interpretation of "Adjusted R

Square" (adj. R2 ) is another important factor. A value of .803

(coefficients table) in this example indicates true 80.3% of

variation in the outcome variable is explained by the

predictors which are to keep in the model. High discrepancy

between the values of R-squared and Adjusted R

Squareindicates a poor fit of the model. Any addition of

useless variable to a model causes a decrease in adjusted r-

squared. But, for any useful variable added, adjusted r-

squared will increase. Adjusted R2 will always be less than

or equal to R2. Adjusted R2 therefore, adjusts for the number

of terms in a model. As R2 always increases and never

decreases, it can appear to be a better fit with the more terms

added to the model and the adjusted R2 penalizes one from

being completely misleading.

Stephanie (2018) cautions about how to differentiate

between R2 and adjusted R2 . R2 Shows how well data points

fit a regression line assuming every single variable explains

the variation in the dependent variable which is not true.

Whereas, adjusted R2 tells how well the data points fit a

regression line showing the percentage of variation

explained only by the independent variables that actually

affect the dependent variable. In addition, example of

interpreting and applying a multiple regression model

(n.d.)reveals that the "adjusted R²" is intended to "control

for" overestimates of the population R² resulting from small

samples, high collinearity or small subject/variable ratios. Its

perceived utility varies greatly across research areas and

time.

The standard error (in this example .55)of a model fit is a

measure of the precision of the model. It is the standard

deviation of the residuals. It shows how wrong one could be

if s/he used the regression model to make predictions or to

estimate the dependent variable or variable of interest. As R²

increases the standard error will decrease. On average, our

International Journal of Science and Research (IJSR)

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estimates of hours per week with this model will be wrong

by .55which is not an ignorable amount given the scale of

hours per week. And hence, the standard error is wished to

be as small as possible. The standard error is used to get a

confidence interval for the predicted values.

Correlated predictors (multicollinearity) may cause large

standard error of the estimate of the regression coefficient.

However, even with the presence of multicollinearity the

regression can still be precise if the "magnified" standard

error is still small enough.

Statistical significance of the model

The F-ratio in the ANOVA (Table 3) tests whether the

overall regression model is a good fit for the data. The table

shows that the independent variables statistically

significantly predict the dependent variable, F (3, 8) =

15.907, p (.001) < .05 (i.e., the regression model is a good fit

of the data).

Table 3: ANOVA

ANOVAa

Model Sum of Squares df Mean Square F Sig.

1 Regression 14.274 3 4.758 15.907 .001b

Residual 2.393 8 .299

Total 16.667 11

a. Dependent Variable: hours per week

b. Predictors: (Constant), husband‟s years of education ,

wife‟s years of education, no. of children

Statistical significance of the independent variables

Statistical significance of each of the independent variables

tests whether the unstandardized (or standardized)

coefficients are equal to 0 (zero) in the population(i.e. for

each of the coefficients, H0 : β = 0 versus Ha: β ≠ 0 is

conducted). If p < .05, the coefficients are statistically

significantly different to 0 (zero). The usefulness of these

tests of significance are to investigate if each explanatory

variable needs to be in the model, given that the others are

already there.

Table 4: Coefficients

Coefficientsa

Model Unstandardized

Coefficients Standardized

Coefficients t Sig. Correlations Collinearity Statistics

B Std. Error Beta Zero-order Partial Part Tolerance VIF

(Constant) 2.021 1.681 1.203 .263

No. of children .367 .185 .348 1.984 .082 .759 .574 .266 .584 1.711

Wife‟s year of education .271 .080 .491 3.386 .010 .641 .767 .454 .853 1.173

Husband‟s years of education -.211 .081 -.425 -2.584 .032 -.653 -.675 -.346 .663 1.509

a. Dependent Variable: hours per week

Given that, the t -value and corresponding p-value are in the

"t" and "Sig." columns ( Table 4) , respectively, in this

example, the tests tell us that wife's years of education

p(.010)<0.05 and husband's years of education

p(.032)<0.05 are significant , but no of children is not

significant P(.082)>0.05. This means that the explanatory

variable no of children is no more useful in the model, when

the other two variables are already in the model. In other

words, with wife's years of education and husband's years

of education in the model, no of children no more adds a

substantial contribution to explaining hours per week.

Like the standard error of model fit discussed above, the

standard error of the coefficients in regression output are

also wished to be as small as possible. It reflect show wrong

you could be, while estimating its value. For instance, in this

example relative to the coefficient .271 of wife's years of

education its standard error .080 is small.

Estimated model coefficients

The general form of the equation to predict hours per

week from no of children, wife's years of education, and

husband's years of education, is:

Predicted hours per week = 2.021 + 0.367 ( no of children) +

0.271(wife's year of education) – 0.211 ( husband's years of

education)

This is obtained from the (Table 5) below:

Table 5: Coefficients

Model Unstandardized

Coefficients Standardized

Coefficients t Sig. Correlations Collinearity Statistics

B Std. Error Beta Zero-order Partial Part Tolerance VIF

(Constant) 2.021 1.681 1.203 .263

No. of children .367 .185 .348 1.984 .082 .759 .574 .266 .584 1.711

Wife‟s year of education .271 .080 .491 3.386 .010 .641 .767 .454 .853 1.173

Husband‟s years of education -.211 .081 -.425 -2.584 .032 -.653 -.675 -.346 .663 1.509

a. Dependent Variable: hours per week

Constant 2.021, is the predicted value for the dependent

variable (in this example)hours per week if all independent

variables, no of children = 0, wife's years of education = 0

and husband's years of education=0. That is, we would

expect an average hour per week of 2.021 husband spends

for house work when all predictor variables take the value 0.

For this reason, this is only a meaningful interpretation if it

is reasonable that the predictors can take the value 0 in

practice. Besides, Karen (2018) reveals that the data set

should include values for all predictors that were near 0.

Therefore, if both of these conditions are not true, the

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constant term (the y-intercept) in the regression line really

has no meaningful interpretation.

However, as it (the y-intercept) places the regression line in

the right place, this is always kept in there while presenting

the regression model. In this example, it is easy to see that in

the data set, no of children sometimes is 0, but both wife's

years of education and husband's years of education, are not

close to 0, then our intercept has no real interpretation.

Unstandardized coefficients indicate how much the

dependent variable varies with an independent variable

when all other independent variables are held constant. The

regression coefficient provides the expected change in the

dependent variable (here: hours per week)for a one-unit

increase in the independent variable. Referring to the

coefficients (Table 5) above the unstandardized coefficient

for no of children is 0.367. This means for every unit

increase (one child increase) in no of children, there is 0.367

hours increase in hours per week. But each one-year increase

in husband's years of education causes reduction (the

negative sign of the coefficient) in hours per week by

0.211hours.

Accordingly, standardized coefficients are called beta

weights, given in the "beta" column. The beta weight

measure how much the outcome variable increases

(in standard deviations) when the predictor variable is

increased by one standard deviation assuming other

variables in the model are held constant. These are useful

measures to rank the predictor variables based on their

contribution (irrespective of sign) in explaining the outcome

variable.

Hence in this case, wife's years of education is the highest

contributing (.491) predictor to explain hours per week, and

the next is husband's years of education (-.425). However,

only when the model is specified perfectly and there is no

multicollinearity among the predictors, Stephanie (2018)

explains.

Zero order partial and part correlation

Table 6: Coefficients

Coefficientsa

Model Unstandardized

Coefficients Standardized

Coefficients t Sig. Correlations Collinearity Statistics

B Std. Error Beta Zero-order Partial Part Tolerance VIF

(Constant) 2.021 1.681 1.203 .263

No. of children .367 .185 .348 1.984 .082 .759 .574 .266 .584 1.711

Wife‟s year of education .271 .080 .491 3.386 .010 .641 .767 .454 .853 1.173

Husband‟s years of education -.211 .081 -.425 -2.584 .032 -.653 -.675 -.346 .663 1.509

a. Dependent Variable: hours per week

Zero order correlation are the bivariate correlation between

the predictors and the dependent variable. Hence .759 in this

example is the direct effect of no of children on hours per

week, this ignores the effect of other two predictor variables

that may/may-not be influencing the dependent variable.

But when the effect of the other two independent variables

are accounted (but kept constant) to no of children and hours

per week, the correlation changes to be less strong.574,

which is partial correlation. And, For the same case, the part

correlation .266 is the correlation between no of children and

hours per week where the effect of the other two

independent variables are completely excluded out.

From the causal perspective, this means (in this example) if

we ch ange no of children , we change the other variables,

too. Now, when we model the TOTAL effects from no of

children on hours per week, we have to account for the

direct effect (which appears to be strong) and the indirect

effect of no of children influencing the other variables which

in turn influence hours per week. When we combine the

strong direct impact with the indirect effects, we end up with

an overall "weaker" impact.

Because part correlations are the correlations that presume

the effect of the other predictors have been excluded out,

these are helpful to identify if the multiple regression used

was beneficial. I.e. to estimate gain in predictive ability

(how much gain had been there in the predictive ability due

to the combination of the predictors in the model) of the

model. In this example, part coefficients of determination

(SPSS does not produce this) are (.266)2, (.454)2 and (-.346)2

respectively for the predictors no of children, wife's years of

education, and husband's years of education . These unique

contributions of the predictors when added up, approximates

(7.1+20.6+12) = 39.7% of the variation in the outcome

variable. And this percentage of variance in the response

variable is different from the R-squared value (85.6 %) in

the model. Meaning that (85.6-39.7 =45.9) 46% overlapping

predictive work was done by the predictors. Which is not

that bad. This proves the combination of the variables had

been quite good.

The information in the (Table 6) above also allows us to

check for multicollinearity. A common rule of thumb: for

any predictor VIF > 10 should be examined for possible

multicollinearity problem (Dhakal, 2016). In our multiple

linear regression model. VIF should be < 10 (or Tolerance >

0.1) for all variables, which they are.

4. Summary

Putting the above all together we could write up the results

as follows:

A multiple regression was run to predict hours per week a

husband spends at house work, from no of children, wife's

years of education and husband's years of education. The

model statistically significantly predicted hours per week F

(3, 8) = 15.907, p(.001) < .05, R2 = 0.856 . Out of three only

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two variables wife's years of education p (.010)< .05 and

husband's years of education p (.032)< .05 added

statistically significantly to the prediction. The highest

contributing predictor is wife's years of education (.491)

and, and the next is husband's years of education (-.425) to

explain hours per week. Multicollinearity problem does not

exist in the model as VIF for all variables is < 10 (or

Tolerance > 0.1). And, 46 % overlapping predictive work

was done by the predictors. This proves the combination of

the variables had been quite good.

No of children is not significant P (.082)>0.05, has therefore

no substantial contribution in explaining hours per week,

when the other two significant predictors are already in the

model. Dare to answer the questions new experiment will

pose, when the study is replicated with only the two

significant predictors?

5. Conclusion

The demonstration of interpreting of multiple regression

output obtained through SPSS is descriptive and intuitive.

Henceforth, it can be used by the researchers, students, and

the related faculties as a template while each one of the

related would be using real data for problem solving

researches and the studies.

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... According to Paille & Mucchielli (2003), loyalty is defined as the degree to which the research instruments used consistently measure the construct studied, whereas the validity corresponds to the degree to which the research instruments used measure perfectly the constructed studied. Factorial analysis as the main component will make it possible to verify, in part, the validity of our constructs and the alpha of Cronbach, the reliability of our constructs (Dhakal, 2018). ...

... To study the relationships between the dependent variable and each of the independent variables, regression analysis is performed. This method is an analysis that presents the direction and shape of the relationship between a continuous dependent variable (simple regression) or several independent variables (multiple regression) (Dhakal, 2018). In the case of this article, the dependent variable is loyalty, while the independent variables are trust, satisfaction, commitment, and communication (Table 6). ...

... For the analysis of simple regression, we used two elements to assess the relationship between our dependent variable which is loyalty, and independent variables (Dhakal, 2018). Table 7 shows that the model relating consumer confidence in the bank to loyalty is significant, with p(F0) = .000. ...

  • Chiraz. Rouissi Chiraz. Rouissi

In recent years, the marketing of services, long in search of academic legiti-macy, has found a clear recognition of its specificities. Banking marketing, a component of the services sector, is getting a promising boost from this de-velopment. The present research is proposed to study the development of the activity of banking strategies and customer loyalty introduced in banks to enable them to optimize the quality of communication and satisfaction while generating more profits and trust. Keywords Banking Marketing, Satisfaction, Trust, Loyalty, Communication (18) (PDF) Banking Strategies and Customer Loyalty Case of Tunisian Banks. Available from: https://www.researchgate.net/publication/350492641_Banking_Strategies_and_Customer_Loyalty_Case_of_Tunisian_Banks [accessed Sep 08 2021].

... Multiple regression analysis and individual linear regression prediction models were performed using Statistical Package for Social Sciences v: 26.0 (SPSS IBM, Armonk, NY, USA). This software verified data which was expressed as mean ± standard error by one way analysis of variance (ANOVA) with significance set at p < 0.05 (Sowndarya and Doss, 2017;Dhakal, 2019;. ...

  • Dharaniyambigai Kuberapandian Dharaniyambigai Kuberapandian
  • Victor Arokia Doss

Cardiac hypertrophy (CH), leading to cardiac failure is due to chronic metabolic alterations occurring during cellular stress. Besides the already known relationship between oxidative stress and CH, there are implications of reductive stress leading to CH. This study attempted to develop reductive stress-based CH rat model using n-acetyl-L-cysteine (NAC), a glutathione agonist that was compared with typical isoproterenol (ISO) induced CH model. The main objective was to identify serum metabolites that can serve as potent predictors for seven routine clinical and diagnostic parameters in CH: 3-hydroxybutyrate (3-HB), lactic acid (LA), urea, and ECG-CH parameters (QRS complex, R-amplitude, R-R interval, heart rate) that were hypothesized to underlie metabolic remodelling in this study. CH was assessed using electrocardiography, hypertrophic index and histopathological analysis (H&E stain) in both ventricles after 2 weeks. Gas chromatography mass spectroscopy analysis (GC-MS) identified unique metabolite finger-prints. Correlation and pattern analysis revealed strong relationships between specific metabolites and parameters (Pearson's score > 0.7) of this study. Multiple regression analysis (MRA) for the strongly related metabolites (independent variables) with each of the seven parameters (dependent variables) identified significant predictors for the latter namely fructose, valine, butanoic acid in NAC and cholesterol, erythrose, isoleucine in ISO models, with proline and succinic acid as common for both models. Metabolite set enrichment analysis (MSEA) of those significant predictors (p < 0.05) mapped butyrate metabolism as highly influential pathway in NAC, with arginine-proline metabolism and branched chain amino acid (BCAA) degradation as common pathways in both models, thus providing new insights towards initial metabolic remodeling in the pathogenesis of CH.

... Multiple regression analysis and individual linear regression prediction models were performed using Statistical Package for Social Sciences v: 26.0 (SPSS IBM, Armonk, NY, USA). This software verified data which was expressed as mean ± standard error by one way analysis of variance (ANOVA) with significance set at p < 0.05 (Sowndarya and Doss, 2017;Dhakal, 2019;. ...

... represents for the quality of Maximum Power demand (Pmax) is not a good level of prediction. However, a Small R 2 value is not always a problem [14]. The value of R2 = .042 ...

  • Virak Dy
  • Naraphorn Paoprasert Naraphorn Paoprasert

Recently, there are many factors affecting electricity demand in different ways. The relation between electricity demand and economic, demographic, increasing new consumer connection, technological, climate, and government policies on electricity price, etc. This study aimed to identify the main factors that affect electricity demand and observed which factors had more relation affecting on electricity demand in Cambodia. The first method of defining relation to predicting annual power demand in the future on economic factors based on annual data from 2004 to 2018. The method was paring GDP with power demand delivered using regression analysis, then with GDP and Total consumer connection by multi-regression analysis. Secondly, for environmental factors affecting on predicting daily maximum power demand (P max ) by temperature and humidity from 1 st Jan 2020 to 20 th July 2020, using regression and multi-regression respectively. As a result of linear regression, we observed annual new consumer connection and GDP of Cambodia were the best factors affecting electricity demand. However, for environmental factors, temperature and humidity are not really affect the curve of (P max ) from our data. Daily temperature in Cambodia could be explained only 4.2% of daily maximum electricity demand while humidity was not significant.

... Smaller values of R 2 may not necessarily be insignificant, although caution must be exercised in interpretation without being combined with other statistical methods. However, based on the knowledge of the subject area in studies of human behaviour, which are difficult to predict, a high value of R 2 has been described as being 'almost impossible' [11]. Given this caveat, the results at least show a trend that can be further studied. ...

  • Sudhir Kumar Pasala Sudhir Kumar Pasala
  • Lakshmi Gumpeny
  • Madhu Kosuri
  • GR Sridhar

In an effort to arrest the spread of coronavirus (COVID-19) infection, a nationwide lockdown was declared in India in March 2020. To assess how personal built environments affected the citizens in the first few weeks, an explorative online survey was conducted, eliciting responses about work habits before the lockdown, psychological wellbeing, time spent in various activities, characteristics of those who worked from home, and food and sleep patterns. We received 121 (76 male and 45 female) responses with an average age of 35.5 years [max: 70 years, min: 18 years, standard deviation (SD): 12.9 years]. The major difference caused by the lockdown was a reduction in the time taken and distance travelled of the commute to workplaces, which was an average of 30 minutes and 9.5 km, respectively. In terms of diet, subjects who were vegetarian did not experience any difference, unlike those who were non-vegetarians ( p < 0.05). The results show an association of the dependent variable of 'feeling in general' with predictor variables of 'energy, pep, vitality' and 'feel healthy to work' during the pandemic, whereas the predictor variables of 'energy, pep, vitality', 'happy and satisfied personal life', 'feel healthy to work' show an association with the dependent variable of 'feeling in general' before the lockdown with a significance of p < 0.02 and R ² = 0.51 and R ² = 0.60, respectively. Among those who worked from home in constrained environments, people found spaces and seemed to adapt reasonably well to the built environment with employees showing a preference for working from bedrooms and students for working from 'sit-out' (outside) spaces ( p < 0.05). There was no change in the quality or quantity of sleep during the lockdown. This study in the early weeks of the lockdown documents the way in which individuals lived through it in terms of the built environment at home.

... For descriptive analysis, it was divided into two parts: the first part is descriptive analysis to describe the characteristics of respondents included age, gender, occupation, income, occupation, likely travel, travel plan, and the second part is to explain the distribution of the variables used in this study. Quantitative analysis in this study uses multiple linear regression analysis, with the following steps: a) the linear regression equation, this step is to find a linear regression equation to a measured relationship among X and Y variables (Dhakal, 2018); b) f test, to find out there a significant simultaneous relationship between variables X and variable Y (Sugiyono, 2007); c) t-test, to find out there a significant partial impacts of variables X to variable Y (Kim, 2005), d) standardized beta, to find out which variables independent is dominant influence variable dependent (Shadab et al, 2018); e) r-squared in the regression model was used to examine statistically the proportions of variance described in a study (Cohen et al., 2003). ...

Purpose: Several industries affected by the Covid-19 outbreak – one of the most affected is the tourism industry due to travel restrictions, which have resulted in an unprecedented slump in the number of international tourists. This situation has an impact on changing consumer behavior towards intention to travel. This study aims to measure the impact of Covid-19 on international tourists' consumer behavior towards crises to intention to travel overseas after the pandemic is over. Research methodology: A paper questionnaire was distributed to international tourists who have been traveling abroad (outside country of origin) at least once during the last 12 months through a nonprobability, convenience-sampling approach. A total of 350 questionnaires were analyzed using multiple regression linear. Results: The results from the regression model suggest that: (1) general impact have significant partial effects on traveling intention; (2) attitude and preference have a significant partial impact to travel intention; (3) hygiene and safety have significant partial impacts to travel intention; (4) general impact, attitude, and preference, hygiene and safety have a significant simultaneous impact to travel intention. Implications and future research issues were discussed. Limitations: This research is limited due to the limited number of respondents. Contribution: This research suggests that every country carries out promotions and increases national branding to rebuild trust to travel. Keywords: Impact, Covid-19, Customer behavior, International tourists, Travel intention, Post-pandemic

... Nevertheless, small R 2 values are not necessarily always problematic, and high R 2 values are not necessarily good (Frost, 2017). For instance, a high value R 2 is mostly impossible for human behaviour variables, because it is very hard to predict; and does not mean a predicted model in such a situation is valueless (Dhakal, 2019). Though the multiple linear regression shows that the independent variables are correlated with the dependent variable, the model shows no statistical significant association between the independent variables and dependent variables, P > 0.05. ...

The Coronavirus Disease pandemic has affected over 200 countries, including Nigeria; and its psychological impacts demands on HCWs are among crucial considerations owing to the fact that occurrence of acute stress needs adaptive response to meet those demands. However, critical studies on the interrelatedness and importance of challenges, coping strategies and resilience during the pandemic are lacking. Objective: To investigate Covid-19 pandemic challenges, coping strategies and resilience among healthcare workers using multiple linear regression analysis. Method: This was a descriptive cross-sectional survey among health workers in a State in Northern Nigeria. Data collection was executed through the use of google form software. One hundred and forty-three health care workers constituted the sample. Questionnaires were used for data collection. A combination of consecutive and convenient sampling methods were used. Data analysis was by Statistical Product and Service Solutions (SPSS) version 25. Findings: Most of the respondents (89.5%) were having very high challenges. Most of the coping strategies of the respondents centered at low to moderate level (35.7% and 37.1%) respectively; and majority (27.3%) had very low resilience. The correlation between Covid-19 challenges (predictor variable 1) and Covid-19 resilience (outcome variable) was 0.119. The correlation between the Covid-19 coping strategy (predictor variable 2) and Covid-19 resilience (outcome variable) was 0.181. Moreover, the correlation between the predictor variables themselves is 0.301. The result indicated that the model was not a significant predictor of HCWs resilience. The model shows that F (2, 140) = 2.71, P = 0.07. R was 0.19, and R 2 was 0.037. There was no statistical significant contribution to the prediction of HCWs resilience from the individual predictors. For challenges of Covid-19 variable (B = 0.080, P = 0.413) and for coping strategies of Covid-19 variable (B = 0.235, P = 0.069).

α-Mangostin is one of the secondary metabolites in mangosteen pericarp, which has been reported to have anti-breast cancer activity. In our previous study, three α-mangostin derivatives were computationally designed as hERα antagonists. In this present study, the designed compounds were synthesized undergoing a benzoylation reaction between α-mangostin with three benzoyl chloride derivatives to produce three derivatives, namely, AMB-1, AMB-2, and AMB-10. The synthesized compounds were then evaluated for their antiproliferative activity against the MCF-7 breast cancer cell model with hERα as the protein target. The in vitro assay shows moderate activity (57-126 μM) for all derivatives. The dynamic behaviors of all ligands, including α-mangostin and 4-hydroxytamoxifen (4-OHT), were studied with 100 ns of MD simulation. The structure-activity relationship shows that although it does not entirely concord with the expected design, it can explain the trend of α-mangostin and its derivatives antiproliferative activities against MCF-7, which associates with hERα antagonism.

College students experience high levels of examination stress due to various reasons such as lack of examination preparation, incompletion of syllabus, students' study style, memory capacity and lack of necessary information. Stress is the response of pressure. Sometimes the pressure about the exams may cause the stress. Most of the college students are under stressed. College students are having a stress from various segments that from their own family, friends, relatives and neighbors and from their colleagues, from professors, from society and also from their examination. Majority of the students are experiencing various levels of examination stress for their number of different reasons. When stress is felt negatively or becomes extreme, it leads to anxiety before, during and after exams and in due course affects their academic activities as well as achievement. These exam stresses are cause students to feel depressed and affects their sleep, eating, mood, and behaviors. In order to obtain reliable data, a total of 460 samples from the College of Education were collected from a structural Questionnaire (link) was sent to students via Whatsapp and email using the "Google-Form". The data were analyzed with the help of descriptive and hypothetical statistical techniques. The Software Package for Social Sciences facilitated the data calculation process. This study shows that there is significant linear relationship between an Examination Stresses and Courses of Study or not. The researcher has applied the statistical tools like percentage analysis, reliability test, factor analysis and regression analysis to analyse the results. The researchers' conclude their study that there is no significant linear relationship between an Examination Stresses and students' Courses of Study. The examination stress are depends on the students mindset, professors teaching style and the correction method and mark or grade system. In case the students are preparing well in exam, they have lesser stress compare with others.

  • Chuda Dhakal Chuda Dhakal

p> Background: Fitting a multiple regression model is always challenging and the level of difficulty varies according to the purpose for which it is fitted. Two major difficulties that arise while fitting a multiple regression model for forecasting are selecting 'potential predictors' from numerous possible variables to influence on the forecast variable and investigating the most appropriate model with a subset of the potential predictors. Objective: Purpose of this paper is to demonstrate a procedure adopted while fitting multiple regression model (with an attempt to optimize) for rice production forecasting in Nepal. Materials and Methods: This study has used fifty years (1961-2010) of time series data. A list of twenty-one predictors thought to impact on rice production was scanned based upon past literature, expert's hunches, availability of the data and the researcher's insight which left eleven possible predictors. Further, these possible predictors were subjected to family of automated stepwise methods which left five 'potential predictors' namely harvested area, rural population, farm harvest price, male agricultural labor force and, female agricultural labor force. Afterwards, best subset regression was performed in Minitab Version 16 which finally left three 'appropriate predictors' that best fit the model namely harvested area, rural population and farm harvest price. Results: The model fit was significant with p < .001. Also, all the three predictors were found highly significant with p < 0.001. The model was parsimonious which explained 93% variation in rice production with 54% overlapping predictive work done. Forecast error was less than 5%. Conclusion : Multiple regression model can be used in rice production forecasting in the country for the enhanced ease and efficiency. Nepalese Journal of Statistics, Vol. 2, 89-98</p

Multiple regression (MR) analyses are commonly employed in social science fields. It is also common for interpretation of results to typically reflect overreliance on beta weights (cf. Courville & Thompson, 2001; Nimon, Roberts, & Gavrilova, 2010; Zientek, Capraro, & Capraro, 2008), often resulting in very limited interpretations of variable importance. It appears that few researchers employ other methods to obtain a fuller understanding of what and how independent variables contribute to a regression equation. Thus, this paper presents a guidebook of variable importance measures that inform MR results, linking measures to a theoretical framework that demonstrates the complementary roles they play when interpreting regression findings. We also provide a data-driven example of how to publish MR results that demonstrates how to present a more complete picture of the contributions variables make to a regression equation. We end with several recommendations for practice regarding how to integrate multiple variable importance measures into MR analyses.

  • J. Scott Armstrong J. Scott Armstrong

Soyer and Hogarth's article, 'The Illusion of Predictability,' shows that diagnostic statistics that are commonly provided with regression analysis lead to confusion, reduced accuracy, and overconfidence. Even highly competent researchers are subject to these problems. This overview examines the Soyer-Hogarth findings in light of prior research on illusions associated with regression analysis. It also summarizes solutions that have been proposed over the past century. These solutions would enhance the value of regression analysis.

  • George P. McCabe Jr

Linear models are often used to quantify differentials between protected and unprotected groups on variables such as salary. Some consequences of model misspecification are examined. In addition, the effects of preferential selection on linear analysis results are studied.

  • Fred S. Guthery
  • Ralph L. Bingham

We perceive a need for more complete interpretation of regression models published in the wildlife literature to minimize the appearance of poor models and to maximize the extraction of information from good models. Accordingly, we offer this primer on interpretation of parameters in single- and multi-variable regression models. Using examples from the wildlife literature, we illustrate how to interpret linear zero-intercept, simple linear, semi-log, log-log, and polynomial models based on intercepts, coefficients, and shapes of relationships. We show how intercepts and coefficients have biological and management interpretations. We examine multiple linear regression models and show how to use the signs (+, -) of coefficients to assess the merit and meaning of a derived model. We discuss 3 methods of viewing the output of 3-dimensional models (y, x1, x2) in 2-dimensional space (sheet of paper) and illustrate graphical model interpretation with a 4-dimensional logistic regression model. Statistical significance or Akaike best-ness does not prevent the appearance of implausible regression models. We recommend that members of the peer review process be sensitive to full interpretation of regression models to forestall bad models and maximize information retrieval from good models

  • Paul Dion Paul Dion

This article briefly review the fundamentals of structural equation modeling for readers unfamiliar with the technique then goes on to offer a review of the Martin and Cullen paper. In summary, a number of fit indices reported by the authors reveal that the data do not fit their theoretical model and thus the conclusion of the authors that the model was "promising" are unwarranted.

How to interpret R-squared in regression analysis

  • J Frost

Frost, J. (2017). How to interpret R-squared in regression analysis. Retrieved fromhttp://statisticsbyjim.com/regression/interpret-rsquared-regression/ Accessed on 02 June 2018.

Interpreting the results from multiple regression and stru ctural equation models

Interpreting the results from multiple regression and stru ctural equation models. Bulletin of the Ecological Society of America, 86(4), 283 -295. ISSN:0012-9623, EISSN:2327-6096, doi: 10.1890/0012-9623(2005)86[283:ITRFMR]2.0.CO;2