Question

Suppose I am trying to guess the salary of one of my fellow professors who I think is 40 years old, has been at xxuniversity for 5 years, and has 25 publications. I am provided with the following regression analysis results from several alternative models that predict salary (in CAD) from these variables, based on N=35 participants. Note: yrs = years.

Model 1; R-squared = 0.578; Adjusted R-squared = 0.537

	Coefficient	Standard Error	t	p-value
Intercept	86248.19	10016.43	8.61	0.00
Age (in yrs)	364.86	130.59	2.79	0.01
Yrs at McGill	-714.21	124.08	-5.76	0.00
Publications	-129.16	134.33	-0.96	0.34

Model 2; R-squared = 0.566; Adjusted R-squared = 0.538

	Coefficient	Standard Error	t	p-value
Intercept	79024.01	6616.08	11.94	0.00
Age (in yrs)	381.64	129.27	2.95	0.01
Yrs at McGill	-724.08	123.51	-5.86	0.00

Model 3; R-squared = 0.472; Adjusted R-squared = 0.439

	Coefficient	Standard Error	t	p-value
Intercept	106643.02	7553.03	14.12	0.00
Yrs at McGill	-695.56	136.44	-5.10	0.00
Publications	-179.32	146.60	-1.22	0.23

Model 4; R-squared = 0.127; Adjusted R-squared = 0.073

	Coefficient	Standard Error	t	p-value
Intercept	80785.00	14116.02	5.72	0.00
Age (in yrs)	324.42	184.60	1.76	0.09
Publications	-193.16	189.52	-1.02	0.32

In the space below, answer the following questions with each response numbered and on a separate line.
1. Based on the results above, which model is the best parsimonious model?
2. Why did you choose this model?
3. Using your chosen model, what is the predicted value of salary in CAD for my colleague? (only final answer required)
4. Using your chosen model, provide a detailed interpretation of the intercept.
5. Using your chosen model, provide a detailed interpretation of one other regression coefficient in the model.
6. Using your chosen model, provide a detailed interpretation of R-squared.

Answer 1

1. Bsed on the results model2 is the best.

2. Since, model 2 has the highest adjusted R^2 and lowest standard errors among all the models .

3. Here, the professor is 40 years old, has been at xxuniversity for 5 years, and has 25 publications. So, based on the model coefficient values we get ,

salary= 79024.01+381.64*40-724.08*5 = 90,669.21

4. The intercept of a regression model is the expected mean value of dependent variable when all independent variable=0. That means when age and years at that university is 0, salary will be 79024.01 units.

5. From coefficients of the model we get,

for 1 unit change in age, salary will increase by 381.64 units and for 1 unit change in yrs at M.c gill university , salary will fall down by 724.08 units.

6. Here, R^2 in the model is 0.566 . That means 56.6% variation can be explained by this fitted regression line among all the variation.