Econometric: chapter 3: Multiple Regression Analysis Estimation

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5 In a study relating college grade point average to time spent in various activities, you distribute a sur- vey to several students. The students are asked how many hours they spend each week in four activi- ties: studying, sleeping, working, and leisure. Any activity is put into one of the four categories, so that for each student, the sum of hours in the four activities must be 168. (i) In the model GPA = Bo + Bistudy + Bysleep + Bywork + Baleisure + 4, does it make sense to hold sleep, work, and leisure fixed, while changing study? (ii) Explain why this model violates Assumption MLR.3. 106 PART 1 Regression Analysis with Cross-Sectional Data (iii) How could you reformulate the model so that its parameters have a useful interpretation and it satisfies Assumption MLR.3?16 The following equations were estimated using the data in LAWSCH85: Isalary = 9.90 - .0041 rank + .294 GPA (.24) (.0003) (.069) n = 142, R2 = .8238 Isalary = 9.86 - .0038 rank + .295 GPA + .00017 age (.29) (.0004) (.083) (.00036) n = 99, R= = .8036 How can it be that the R-squared is smaller when the variable age is added to the equation?Step 2 The value of R? is 0.8238 for first equation which indicates that fit of the model. This shows that there is 82.38% of the variance in the dependent variable is collectively explained by the independent variables in the model. The value of R? is 0.8036 for second equation which indicates that fit of the model. It indicates that there is 80.36% of the variance in the dependent variable is collectively explained by the independent variables in the model. Main reason of decreased R? is that the independent variable is not explaining much variation of dependent variable, here age is the independent variable and salary is the dependent variable, as variable age is added to model RZ decreased since age is not explaining much variation as compared to other variables like rank and GPA. Step 1 From the provided information, Two models are; Isalary =9.90 -0.0041 rank + 0.294 GPA Where n=142, R2-0.8238 Isalary =9.86-0.0038 rank + 0.295 GPA + 0.00017 age Where n=99, R2=0.8036