Question

Please use R or Rstudio for this exercise and show everything, including the R output. Pay attention in everything in Bold, please.

" The data in stat5_prob2 contains values of the following four variables for 93 employees of Harris Bank Chicago in 1977:

• y : beginning salary in dollars (SALARY)
• x1 : years of schooling at the time of hire (EDU)
• x2 : number of months of previous work experience (EXPER)
• x3 : number of months after January 1, 1969, that the individual was hired (TIME)

Fit a multiple linear regression model on SALARY using the three explanatory variables to answer the following questions. (Note: Recall, when you read the txt file in R, indicate header=T since there is a title for each column, and also use sep=’,’ since the columns are separated with a comma. That is, use

  salaries=read.table(‘stat5_prob2.txt’, header=T, sep=‘,’)
  y=salaries$SALARY

and similarly obtain x1, x2, x3.)

(a) What is the estimated regression equation relating SALARY to EDUC, EXPER, and

TIME?

(b) Conduct the F test for overall fit of the regression, using a 0.05 significance level.

(c) Is education linearly related to beginning salary (after taking into account the effect of experience and time)? Perform this hypothesis test using 0.05 significance level.

(d) What percentage of the variation in salary has been explained by the regression?

(e) Construct 95% confidence intervals for the regression coefficients β1, β2, β3 and for the variance error term σ2.

*** Here is the data stat5_prob2***

"SALARY","EDUC","EXPER","TIME"
3900,12,0,1
4020,10,44,7
4290,12,5,30
4380,8,6,7
4380,8,8,6
4380,12,0,7
4380,12,0,10
4380,12,5,6
4440,15,75,2
4500,8,52,3
4500,12,8,19
4620,12,52,3
4800,8,70,20
4800,12,6,23
4800,12,11,12
4800,12,11,17
4800,12,63,22
4800,12,144,24
4800,12,163,12
4800,12,228,26
4800,12,381,1
4800,16,214,15
4980,8,318,25
5100,8,96,33
5100,12,36,15
5100,12,59,14
5100,15,115,1
5100,15,165,4
5100,16,123,12
5160,12,18,12
5220,8,102,29
5220,12,127,29
5280,8,90,11
5280,8,190,1
5280,12,107,11
5400,8,173,34
5400,8,228,33
5400,12,26,11
5400,12,36,33
5400,12,38,22
5400,12,82,29
5400,12,169,27
5400,12,244,1
5400,15,24,13
5400,15,49,27
5400,15,51,21
5400,15,122,33
5520,12,97,17
5520,12,196,32
5580,12,133,30
5640,12,55,9
5700,12,90,23
5700,12,117,25
5700,15,51,17
5700,15,61,11
5700,15,241,34
6000,12,121,30
6000,15,79,13
6120,12,209,21
6300,12,87,33
6300,15,231,15
4620,12,12,22
5040,15,14,3
5100,12,180,15
5100,12,315,2
5220,12,29,14
5400,12,7,21
5400,12,38,11
5400,12,113,3
5400,15,18,8
5400,15,359,11
5700,15,36,5
6000,8,320,21
6000,12,24,2
6000,12,32,17
6000,12,49,8
6000,12,56,33
6000,12,252,11
6000,12,272,19
6000,15,25,13
6000,15,36,32
6000,15,56,12
6000,15,64,33
6000,15,108,16
6000,16,46,3
6300,15,72,17
6600,15,64,16
6600,15,84,33
6600,15,216,16
6840,15,42,7
6900,12,175,10
6900,15,132,24
8100,16,55,33

Answer 1

this image has all the solution. for part (c):- education is linearly dependent to salary because null hypothesis is rejected.