show all the steps please, thanks An economics department at a large state unive
ID: 3217478 • Letter: S
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show all the steps please, thanks
An economics department at a large state university keeps track of its majors' starting salaries. Does taking econometrics affect starting salary? Let SAL = salary in dollars, GPA = grade point average on a 4.0 scale, METRICS = 1 if the student took econometrics, 0 otherwise. Using data on 50 recent graduates, we obtain the estimated regression: E (SAL) = 24200 + 1643 GPA + 5033 METRICS, R^2 = 0.74 a. Interpret the estimated equation. b. How would you modify the equation to see whether women had lower starting salaries than men? (Define the indicator variable FEMALE = 1 if female; 0 otherwise.)Explanation / Answer
(a)
the following regression equation can be interpretted in the following way,
The intercept of the equation is 24200. The coefficient of the GPA is 1643 implying that the GPA score have a positive effect on the salary i.e. higher the GPA score higher the salary. The 2nd factor that is whether they have taken econometrics or not also have a positive effect on the salary with a high positive coefficient of 5033. Thus the taking econometrics does affect their salary or it can be said that taking econometrics increases their salary (because if the metrics=0, that is not taking econometrics; then the equation reduces to E(sal) = 24200+1643*GPA+5033*0 = 24200+1643*GPA. But if the metrics=1, that is taking econometrics, then the equation is equal to E(sal) = 24200+1643*GPA+5033*1 = 24200+1643*GPA+5033)
Further the R2 value of 0.74 is pretty good and it is a measure of the variation in salary that is explained by the model. It may be explained as 74% of the factors influencing the salary ae explained in the model by the GPA and metrics. The rest 26% of the variation in the salary is due to some other factor or factors which is not included in the model. The R2 value lies between 0 and 1 and the more the value lies close to 1, the better.
(b)
As mentioned, we create an indicator variable Female = 1, if female and 0 otherwise. We then fit a model for the salary using the 3 factors GPA, Metrics and Female. We will obtain coefficients for the 3 factors as in the above case. Now, if the coefficient estimate of Female is negative, then it means that if female(=1), then their salary is reduced by the magnitude of the coefficient and thus they had a less salary than men(=0). If positive, then the female had a higher starting salary than the male workers.
Thus we will get a similar equation like,
E(sal) = 24200+1643GPA + 5033METRICS + a0FEMALE,
where a0 will be obtained by the parameter estimation of regression analysis. The R2 for this model may also be computed.
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