# Multiple Regression Analysis

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Page count 2 573 3 min Economics Essay ðŸ‡ºðŸ‡¸ US

The model summary (Table 1) presents relevant coefficients, which describe how the regression of the model fits the data analyzed. From the table, it is evident that the independent variable, salary per day, and the independent variables, namely, attractiveness, experience, and age, have a multiple correlation coefficient of 0.429. The multiple correlation coefficient indicates that the independent variable and dependent variables have a moderate positive correlation. R-square is a notable coefficient in the model summary table because it is applicable in assessing the predictive power of a regression model. The multiple regression model indicates that attractiveness, experience, and age explain 18.4% of the variability in salary among the models. In this view, R-square has a weak explanatory power because it does not account for 81.6% of the variability in salary among the models. To account for non-predictors in the regression model, the coefficient of adjusted R-square provides reliable information. According to Field (2013), substantial shrinkage of adjusted R-square reduces the generalizability of the model because it indicates that non-predictors exist. Hence, the model summary shows that real predictors explain 17.3% of the variability in salary.

Table 1

 Model Summary Model R R Square Adjusted R Square Std. The error of the Estimate 1 .429a .184 .173 14.57213

The ANOVA table (Table 2) provides important data, which indicates the significance of the model in predicting salary using the attractiveness, experience, and age of the models. F-ratio shows that the regression model is statistically significant in predicting salary, F(3,227) = 17.066, p = 0.000. In this case, the model is very reliable for it provides a good fit for independent variables and the dependent variable.

Table 2

 ANOVA Model Sum of Squares df Mean Square F Sig. 1 Regression 10871.964 3 3623.988 17.066 .000b Residual 48202.790 227 212.347 Total 59074.754 230

Given that the regression model is statistically significant, Table 3 depicts how individual independent variables contribute to the significance of the model.

Table 3

 Coefficients Model Unstandardized Coefficients Standardized Coefficients t Sig. 95.0% Confidence Interval for B B Std. Error Beta Lower Bound Upper Bound 1 (Constant) -60.890 16.497 -3.691 .000 -93.396 -28.384 Age (Years) 6.234 1.411 .942 4.418 .000 3.454 9.015 Experience -5.561 2.122 -.548 -2.621 .009 -9.743 -1.380 Attractiveness (%) -.196 .152 -.083 -1.289 .199 -.497 .104

Table 3 indicates that age and experience are statistically significant predictors of salary (p < 0.000), while attractiveness is an insignificant predictor of salary (p > 0.000). Age is a significant positive predictor of salary because its coefficient is 6.234. The coefficient implies that a year increase in age causes an increase in salary by 6.234 when experience and attractiveness are constant. Experience is a significant negative predictor because its coefficient is -5.561. The coefficient means that a year increase in inexperience as a model results in a decrease of salary by 5.561 when age and attractiveness remain constant. In this view, the regression equation of the model is:

Salary = -60.890 + (6.234Ã—Age) â€“ (5.561 Ã— Experience)

In determining the validity of the model, normality and multicollinearity are significant parameters. The histogram shown in Figure 1 indicates that salary has a negative skewness, which violates the assumption of normality. Moreover, normal P-P plot (Figure 2) confirms that the distribution of salary among models deviates from the normal line. Davis (2013) argues normality errors reduce the reliability of regression models because they violate the assumption of normality. In this view, the model is unreliable because it has inaccuracies, which emanate from normality errors.

## References

Davis, C. (2013). SPSS Step by Step: Essentials for Social and Political Science. New York: Policy Press.

Field, A. (2013). Discovering statistics using SPSS (4th ed.). London: SAGE Publisher.

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EduRaven. 2022. "Multiple Regression Analysis." April 16, 2022. https://eduraven.com/multiple-regression-analysis/.

1. EduRaven. "Multiple Regression Analysis." April 16, 2022. https://eduraven.com/multiple-regression-analysis/.

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EduRaven. "Multiple Regression Analysis." April 16, 2022. https://eduraven.com/multiple-regression-analysis/.

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EduRaven. 2022. "Multiple Regression Analysis." April 16, 2022. https://eduraven.com/multiple-regression-analysis/.

1. EduRaven. "Multiple Regression Analysis." April 16, 2022. https://eduraven.com/multiple-regression-analysis/.

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EduRaven. "Multiple Regression Analysis." April 16, 2022. https://eduraven.com/multiple-regression-analysis/.