Provide a discussion of the results of the multiple regression model requested b

Question

Provide a discussion of the results of the multiple regression model requested by your supervisor, which examines the impact of rule abidance and autonomy (the independent variables) on discretion (the dependent variable), with attention to the direction of relationships, the significance level (p-value) for cach of the independent variables, and the R-squared (see Table 3.3). . Table 3.3 Multiple Regression Results for Dependent Variable of Discretion Beta (standardized coefficient Coefficien Sid. Er. Variable Rule Abidance Autonomy Constant -0.31 0.47 1.94 0.12 0.04 0.28 -2.59 0.010 11.20 0.000 6.88 0.000 0.49 Observations F (2,393) Prob> F R-squared 396 64.08 0,000 0.2459

Explanation / Answer

While fitting a multiple linear regression model, we need to carry out the F test to check for the overall significance of the model.
Here, the p-value of the F test has come out to be 0, which is less than 0.05 (level of significance), signifying that there indeed exists a linear relationship between the two independent variables and the dependent variable.

The R-squared value has come out to be 0.2459. This means that only 24.59% of the variation in the dependent variable is explained by the variation in the two independent variables. This further signifies that the fit of the model is not at all good.

With respect to the independent variable named Rule Abidance, the p-value has come out to be 0.01 which is less than 0.05 = level of significance. This means that this independent variable is significant in the model and thus impacts the value of the dependent variable. Its regression coefficient has come out to be -0.31, which indicates that there is a negative linear relationship between this independent variable and the dependent variable. For every 1 unit increase in the value of Rule Abidance, the value of Discretion decreases by -0.31 units.


With respect to the independent variable named Autonomy, the p-value has come out to be 0.00 which is less than 0.05 = level of significance. This means that this independent variable is significant in the model and thus impacts the value of the dependent variable. Its regression coefficient has come out to be 0.47, which indicates that there is a positive linear relationship between this independent variable and the dependent variable. For every 1 unit increase in the value of Rule Abidance, the value of Discretion increases by 0.47 units.

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