Question

In: Statistics and Probability

Fit a multiple regression model that relates the salary to education, work experience, and time spent...

Fit a multiple regression model that relates the salary to education, work experience, and time spent at the bank so far.

a - State what your model is.

b - Determine whether the independent variables are significant, or not, at a level of significance of 5%.

c - Which independent variable is most significant in explaining salary? Which is least significant?

d - Is your overall model significant? Provide statistical proof by conducting an F-test for overall fit of the regression. State the hypothesis to be tested, the p-value for your F-statistic, and your decision.

The following data is always in the same order.

Salary data, in dollars (n=63):

39000,40200,42900,43800,43800,43800,43800,43800,44400,45000,45000,46200,48000,48000,48000,48000,48000,48000,48000,48000,48000,48000,49800,51000,51000,51000,51000,51000,51000,51600,52200,52200,52800,52800,52800,54000,54000,54000,54000,54000,54000,54000,54000,54000,54000,54000,54000,55200,55200,55800,56400,57000,57000,57000,57000,57000,60000,60000,61200,63000,63000,46200,50400,51000,51000,52200,54000,54000,54000,54000,54000,57000,60000,60000,60000,60000,60000,60000,60000,60000,60000,60000,60000,60000,60000,63000,66000,66000,66000,68400,69000,69000,81000

Education data, in years (n=63):

12,10,12,8,8,12,12,12,15,8,12,12,8,12,12,12,12,12,12,12,12,16,8,8,12,12,15,15,16,12,8,12,8,8,12,8,8,12,12,12,12,12,12,15,15,15,15,12,12,12,12,12,12,15,15,15,12,15,12,12,15,12,15,12,12,12,12,12,12,15,15,15,8,12,12,12,12,12,12,15,15,15,15,15,16,15,15,15,15,15,12,15,16

Previous work experience, in months (n=63):

0,44,5,6,8,0,0,5,75,52,8,52,70,6,11,11,63,144,163,228,381,214,318,96,36,59,115,165,123,18,102,127,90,190,107,173,228,26,36,38,82,169,244,24,49,51,122,97,196,133,55,90,117,51,61,241,121,79,209,87,231,12,14,180,315,29,7,38,113,18,359,36,320,24,32,49,56,252,272,25,36,56,64,108,46,72,64,84,216,42,175,132,55

Previous time spent at the bank data, in months (n=63):

1,7,30,7,6,7,10,6,2,3,19,3,20,23,12,17,22,24,12,26,1,15,25,33,15,14,1,4,12,12,29,29,11,1,11,34,33,11,33,22,29,27,1,13,27,21,33,17,32,30,9,23,25,17,11,34,30,13,21,33,15,22,3,15,2,14,21,11,3,8,11,5,21,2,17,8,33,11,19,13,32,12,33,16,3,17,16,33,16,7,10,24,33

Solutions

Expert Solution

(a) The model is:

y = 31794.798 + 1396.093*x1 + 14.840*x2 + 206.291*x3

(b) All of independent variables are significant.

(c) Education is most significant in explaining salary.

Previous work experience is least significant in explaining salary.

(d) The hypothesis being tested is:

H0: β1 = β2 = β3 = 0

H1: At least one βi ≠ 0

The test statistic is 12.84.

The p-value is 0.0000.

Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the model is significant.

The R code is:

Salary <- c(39000,40200,42900,43800,43800,43800,43800,43800,44400,45000,45000,46200,48000,48000,48000,48000,48000,48000,48000,48000,48000,48000,49800,51000,51000,51000,51000,51000,51000,51600,52200,52200,52800,52800,52800,54000,54000,54000,54000,54000,54000,54000,54000,54000,54000,54000,54000,55200,55200,55800,56400,57000,57000,57000,57000,57000,60000,60000,61200,63000,63000,46200,50400,51000,51000,52200,54000,54000,54000,54000,54000,57000,60000,60000,60000,60000,60000,60000,60000,60000,60000,60000,60000,60000,60000,63000,66000,66000,66000,68400,69000,69000,81000)
Education <- c(12,10,12,8,8,12,12,12,15,8,12,12,8,12,12,12,12,12,12,12,12,16,8,8,12,12,15,15,16,12,8,12,8,8,12,8,8,12,12,12,12,12,12,15,15,15,15,12,12,12,12,12,12,15,15,15,12,15,12,12,15,12,15,12,12,12,12,12,12,15,15,15,8,12,12,12,12,12,12,15,15,15,15,15,16,15,15,15,15,15,12,15,16)
Previousworkexperience <- c(0,44,5,6,8,0,0,5,75,52,8,52,70,6,11,11,63,144,163,228,381,214,318,96,36,59,115,165,123,18,102,127,90,190,107,173,228,26,36,38,82,169,244,24,49,51,122,97,196,133,55,90,117,51,61,241,121,79,209,87,231,12,14,180,315,29,7,38,113,18,359,36,320,24,32,49,56,252,272,25,36,56,64,108,46,72,64,84,216,42,175,132,55)
Previoustimespent <- c(1,7,30,7,6,7,10,6,2,3,19,3,20,23,12,17,22,24,12,26,1,15,25,33,15,14,1,4,12,12,29,29,11,1,11,34,33,11,33,22,29,27,1,13,27,21,33,17,32,30,9,23,25,17,11,34,30,13,21,33,15,22,3,15,2,14,21,11,3,8,11,5,21,2,17,8,33,11,19,13,32,12,33,16,3,17,16,33,16,7,10,24,33)
mod <- lm(Salary ~ Education + Previousworkexperience + Previoustimespent)
summary(mod)

orchestra answered 1 year ago
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