Question

3. (40 points) Use the graph, an output of the least squares prediction equation for the starting salary data (in thousands of dollars) given a graduated student's cumulative GPA, and the table of sampled data below to do the following Student ID GPA(x) 3.26 Starting Salary (y) 33.8 2.60 29.8 3.35 33.5 2.86 30.4 3.82 36.4 2.21 27.6 3.47 35.3 Regression Plot Y= 14.8156 + 5.70657x R-Sq 0.977 寸 853 4.0 2.0 2.5 3.0 3.5 GPA (a) Identify and interpret the least squares point estimates Bo and βί. Does the interpreta- tion of Bo make practical sense? (b) Use the least squares line to obtain a point estimate of the mean starting salary for all marketing graduates having a GPA of 3.25 and a point prediction of the starting salary for an individual marketing graduate having a GPA of 3.25 (c) If a student wishes to obtain a starting salary of $30,000 (hint: y-30), what should their GPA be? (d) Caleulate the necessary quantities such as SSry, SS T, and ỹ, then verify that Bo 14.8156 and 5.70657 by using the formulas in Section 3.2 and outlined in class. (e) Identify SSE. s, and SE, , then calculate the 95% confidence interval for A (f) Test Ho: B1-0 versus Hi B1 0 by setting a 0.05. What do you conclude about the relationship between y and x? (g) Give the 95% confidence interval for a GPA of 3.25 and the 95% prediction interval for a GPA of 3.25 (h) Calculate the quantity SSE then verify that R2 0.977.

Answer 1

a)
b0^ = 14.8156
b1^ = 5.70657

b0^ means the average salary is 14.8156 if the GPA is 0
it does not make practical sense

b1^ means if if GPA increases by 1 unit, the average salary will increase by 5.7066

b)
y^ = 14.8156 + 5.7066*x
= 14.8156 + 5.7066*3.25
= 33.3621

c)
Y^ = 30
30 = 14.8156 + 5.7066*x

d)

Using Excel

x	y
3.26	33.8
2.6	29.8
3.35	33.5
2.86	30.4
3.82	36.4
2.21	27.6
3.47	35.3
xbar	ybar
3.081429	32.4
1.840686	Sxx
10.504	Sxy

Formulas

x	y
3.26	33.8
2.6	29.8
3.35	33.5
2.86	30.4
3.82	36.4
2.21	27.6
3.47	35.3
xbar	ybar
=AVERAGE(A2:A8)	=AVERAGE(B2:B8)
=VAR(A2:A8)*(7-1)	Sxx
=COVARIANCE.S(A2:A8,B2:B8)*6	Sxy

b1^ = Sxy /Sxx = 10.504/1.8406857 = 5.70657

b0^ = ybar - b1^*xbar

= 32.4 - 5.706569 * 3.081428571

= 14.8156

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