Please answer each question item (a through f) in the space provided below. Data
ID: 3268457 • Letter: P
Question
Please answer each question item (a through f) in the space provided below. Data was collected from 40 employees to develop a regression model to predict the employee’s annual salary using their years with the company (Years), their starting salary (Starting), and their Gender (Male = 0, Female = 1). The results from Excel regression analysis are shown below: SUMMARY OUTPUT Regression Statistics Multiple R 0.718714957 R Square 0.516551189 Standard Error 10615.63461 Observations 40 ANOVA df SS MS F Significance F Regression 3 4334682510 1444894170 12.82165585 7.48476E-06 Residual 36 4056901131 112691698.1 Total 39 8391583641 Coefficients Standard Error t Stat P-value Intercept 27946.57894 4832.438706 5.783121245 1.35464E-06 Years 1665.251558 425.0829092 3.917474737 0.000383313 Starting 0.266374185 0.12610443 2.112330112 0.041661598 Gender -3285.541043 5617.145392 -0.584912943 0.56225464 a. What is the regression equation? b. In testing the null hypothesis that the regression equation is not significant at the 0.05 level, what is the appropriate conclusion? c. In testing the significance of the partial regression coefficient associated with the Years variable at the 0.05 significance level, what is the appropriate conclusion? d. In testing the significance of the partial regression coefficient associated with the Starting variable at the 0.05 significance level, what is the appropriate conclusion? e. In testing the significance of the partial regression coefficient associated with the Gender variable at the 0.05 significance level, what is the appropriate conclusion? f. For a male employee with 5 years of experience and a starting salary of $30,000, what is the approximate 95% confidence interval for his annual salary? Arial 3 (12pt) Paragraph Font family Font size Path: p Words:0
Explanation / Answer
a. What is the regression equation?
y^ = 27946.57894 +1665.251558*years +0.266374185*Starting -3285.541043*Gender
b. In testing the null hypothesis that the regression equation is not significant at the 0.05 level, what is the appropriate conclusion?
significance F = 7.48476E-06 < 0.05
hence the regression is significant
c. In testing the significance of the partial regression coefficient associated with the Years variable at the 0.05 significance level, what is the appropriate conclusion?
p-value for years = 0.000383313 < 0.05
hence the variable years is significant
d. In testing the significance of the partial regression coefficient associated with the Starting variable at the 0.05 significance level, what is the appropriate conclusion?
p-value for starting is 0.041661598 < 0.05
hence starting is significant
e. In testing the significance of the partial regression coefficient associated with the Gender variable at the 0.05 significance level, what is the appropriate conclusion?
p-value for Gender = 0.56225464 > 0.05
hence gender is not significant
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