Write the estimated regression equation from the coefficient output and interpret the results. (150 words) Regression Output Model Unstandardized Coefficients Standardized Coefficients t Sig. B Std. Error Beta (Constant) .085 .089 .954 .341 Environment .354 .041 .342 8.613 .000 Brand Diversity -.024 .049 -.020 -.481 .631 Entertainment .401 .044 .368 9.079 .000 Location .291 .043 .272 6.832 .000 Dependent Variable: Consumer Loyalty
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
- Write the estimated regression equation from the coefficient output and interpret the results. (150 words)
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Regression Output |
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Model |
Unstandardized Coefficients |
Standardized Coefficients |
t |
Sig. |
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B |
Std. Error |
Beta |
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(Constant) |
.085 |
.089 |
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.954 |
.341 |
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Environment |
.354 |
.041 |
.342 |
8.613 |
.000 |
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Brand Diversity |
-.024 |
.049 |
-.020 |
-.481 |
.631 |
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Entertainment |
.401 |
.044 |
.368 |
9.079 |
.000 |
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Location |
.291 |
.043 |
.272 |
6.832 |
.000 |
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Dependent Variable: Consumer Loyalty |
- Based on the following output tables, write all the panel data regression models. Which is a better model, FEM or REM? Justify your answer. (200 words)
Table A:
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Dependent Variable: PAYOUT_RATIO |
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Method: Panel Least Squares |
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Variable |
Coefficient |
Std. Error |
t-Statistic |
Prob. |
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FOREIGN_DIRECTORS |
158.8968 |
14.70223 |
10.80766 |
0.0000 |
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FEMALE_DIRECTORS |
-4.463537 |
36.09961 |
-0.123645 |
0.9023 |
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C |
3.143324 |
5.364327 |
0.585968 |
0.5618 |
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Effects Specification |
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Cross-section fixed (dummy variables) |
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R-squared |
0.876583 |
Mean dependent var |
38.31686 |
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Adjusted R-squared |
0.840284 |
S.D. dependent var |
59.89422 |
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S.E. of regression |
23.93641 |
Akaike info criterion |
9.397265 |
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Sum squared resid |
19480.36 |
Schwarz criterion |
9.838894 |
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Log-likelihood |
-200.4385 |
Hannan-Quinn criter. |
9.561900 |
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F-statistic |
24.14892 |
Durbin-Watson stat |
2.351257 |
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Prob(F-statistic) |
0.000000 |
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Table B:
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Dependent Variable: PAYOUT_RATIO |
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Method: Panel EGLS (Cross-section random effects) |
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Variable |
Coefficient |
Std. Error |
t-Statistic |
Prob. |
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FOREIGN_DIRECTORS |
149.4722 |
13.70889 |
10.90330 |
0.0000 |
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FEMALE_DIRECTORS |
17.75043 |
33.50407 |
0.529799 |
0.5990 |
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C |
3.114584 |
11.32865 |
0.274930 |
0.7847 |
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Effects Specification |
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S.D. |
Rho |
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Cross-section random |
30.12334 |
0.6130 |
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Idiosyncratic random |
23.93641 |
0.3870 |
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Weighted Statistics |
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R-squared |
0.749393 |
Mean dependent var |
12.83031 |
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Adjusted R-squared |
0.737459 |
S.D. dependent var |
47.65187 |
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S.E. of regression |
24.41623 |
Sum squared resid |
25038.40 |
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F-statistic |
62.79640 |
Durbin-Watson stat |
1.869314 |
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Prob(F-statistic) |
0.000000 |
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Table C:
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Test cross-section random effects |
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Test Summary |
Chi-Sq. Statistic |
Chi-Sq. d.f. |
Prob. |
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Cross-section random |
3.700706 |
2 |
0.1572 |
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