Question

Description

Here is some data looking at people's salaries, their years of experience, and their average evaluation. Please cut and paste it into excel and run the following regression: Salary = b0 + b1*Experience + b2*Eval Salary Years of experience Average evaluation $ 56,744.30 5 6.85 $ 49,875.12 0 2.92 $ 64,629.44 6 1.69 $ 53,148.67 2 1.89 $ 56,130.69 8 4.93 $ 57,246.71 4 5.87 $ 51,097.09 0 5.09 $ 50,303.00 0 6.42 $ 56,212.37 2 4.2

Instructions

Question 1

What percent of the variance in salary is explained by knowing years of experience and average evaluations?

Answer 1

The given data was taken into Excel and regression analysis was performed. The regression output for the given problem is shown below:

Based on the above summary output, the value of b₀ is 54187.686

The value of b₁ is 1206.386

The value of b₂ is -624.039

R² (Coefficient of determination) is a measure that tells us the percentage of the total variation in the dependent variable that can be explained by the regression model.

In the given problem, the dependent variable is salary. Therefore, on carefully observing the summary output we see that the value of R² is 0.6470 i.e. about 64.70% variation in salary is explained by the regression model.

But, Here the adjusted R² will be better than R² in explaining the variance in salary because in the case of multiple regression models adjusted R² is most useful in explaining the variance in the dependent variable as it takes into account the number of independent variables which are used in the model. Therefore, on carefully observing the summary output we see that the value of adjusted R² is 0.5294 i.e. about 52.94% variation in salary is explained by the regression model. Or we can say that in a true sense, 52.94% of the variance in the salary is explained by knowing the years of experience and average evaluations. The remaining 47.06% variation is unexplained or it may be due to the error term.