Mike Jimenez is president of the teachers' union for Preston School District. In preparing for upcoming negotiations, he would like to investigate the salary structure of classroom teachers in the district. He believes there are three factors that affect a teacher's salary: years of experience, a rating of teaching effectiveness given by the principal, and whether the teacher has a master's degree (0 = No, 1 = Yes). A random sample of 20 teachers resulted in the following data.

Salary ($ Thousands)	Years of Experience	Principal's Rating	Master's Degree
51.1	8	82	0
43.6	5	91	0
39.3	2	62	1
53	15	67	1
48.6	11	73	0
55	14	90	1
52	9	83	0
46.8	7	81	1
58.6	22	70	1
41.7	3	56	1
35.7	1	55	0
40.6	5	82	0
61.8	23	96	1
46.7	17	90	0
48.4	12	54	1
43.6	14	66	0
51.8	8	80	1
40.7	4	54	0
42.8	2	58	1
42.9	8	100	0

Click here for the Excel Data File.Data file should open in a new browswer window. Select "File" then "Save As" to download the file to your computer and be able to use it in Excel.

a.What is the question being asked?(1 point)

b.Label your dependent variable: y = (1 point)

c.Label your independent variables:(1point)

x₁=

x₂=

x₃ =

d.Develop a correlation matrix and state the correlation for each independent variable as it relates to the dependent variable.(2points)(Round all correlation coefficients to 4 decimal places.)

x₁: r=

x₂: r=

x₃: r =

e.Compute and state the regression equation:(2point)(Round the intercept and the regression coefficients to 2 decimal places.)

y = + x₁ + x₂+ x₃

f.What salary would you estimate for a teacher with 12 years of experience, a rating by the principal of 97, and who does not have a master's degree?(1 point)(Round to the nearest dollar)

Salary:

g.What does the value of the Coefficient of Determination tell you about the data?(1 point)

h.Run a diagnosis to deterime if themodelis significant at= 0.05.(Round test statistic to 2decimal places andp-value to 4 decimal places)

h1.Select the correct hypothesis statements.(1 point)

H₀: (Click to select) 1 = 2 = 3 = 0 1 2 3 0 Not all 's = 0

H₁: (Click to select) 1 2 3 0 1 < 2 < 3 < 0 Not all 's = 0

h2.Test Statistic: (1 point)

h3:p-value: (1 point)

h4:What is your decision regarding the null hypothesis?(1 point) (Click to select) Fail to reject the null. Reject the null.

h5:What does this mean? (1 point)

i.Run a diagnosis to determine if the slope of the individual variables are significant at= 0.05.(3points)(Roundp-values to 4 decimal places)

Variable	p-value	Significant (Yes, No)
x1		(Click to select) Yes No
x2		(Click to select) No Yes
x3		(Click to select) No Yes

j.Looking at the standared error of the regression model, what is the prediction range for salary (in $ thousands)?(1 point)(Round to 2 decimal places)+/-

k.Is Multicollinearity a problem? Compute the VIF for each independent variable.(3points)(Round VIF to 3 decimal places)

Variable	VIF	Problem (Yes, No)
x1		(Click to select) No Yes
x2		(Click to select) No Yes
x3		(Click to select) No Yes

l.What conclusions can you draw? Are there any variables you would take out to make it better? Are there any variables you think you might want to include?(1 point)