Question

Mike Jimenesz is president of the teachers' union for preston school district. in preparing for upcoming negotiations, he would like to investigate the salary structure of the classroom teachers in the district. He believes there are three factors that affect a teacher's salary: Years of Experience, Rating of teaching effectiveness given by the principal, and whether the teacher has a master's degree. A random sample of 20 teachers resulted in the following data.

Salary	Years of experience	Principal’s Rating	Master’s Degree
($ thousands)
52.1	8	35	1
43.6	5	43	0
40.3	2	51	0
53	13	60	1
51.6	12	73	1
57	14	80	1
52	9	76	1
46.8	7	54	0
58.6	19	55	1
42.8	3	90	0
36.7	1	30	0
40.6	5	44	0
61.8	23	84	1
54.7	17	76	1
48.4	12	68	0
53.6	14	25	1
51.8	8	90	1
47.7	4	62	0
42.8	1	80	0
53.8	8	72	1
			*1 = yes, 0 = no

Run a diagnosis to see if the model is significant at Alpha=.05

A) State the null and alternate hypothesis

B) Compute the value of the test statistic

C) Compute the P-Value

D) What is your decision regarding the null hypothesis? Interpret the result.

Answer 1

a) The step-by-step instructions to obtain a Multiple linear Regression output using Excel2010 * Store the vari ables is Years of Experience(X). Principal's rating (X,) Master's Degree (X,) and Salary (Y) in the columns of the Excel2010 worksheet * Choose the Data Data Analysis ->Regression * Select the range of the variable Salary(Y) and then select the range of variable Years of Experience (X1), Principal's rating (X2). Master's Degree (X,) * Choose the confidence level is 95% * Tick the labels. * Click ok. The Multiple Linear Regression output using Excel 2010

SUMMARY OUTPUT Rearession Statistics Multiple R R Square Adjusted R Square Standard Error Observations 0.956951431 0.915756042 0.8999603 2.117599947 20 ANOVA Significance F 3 779.9178275 259.972609257.97487 8.14613E-09 MS Regression Residual Total 16 71.74767255 4.484229534 19 851.6655 P-value Lower 95% r95% Lower 95.0%Uer 95.0% 37.918250371.669073075 22.71814874 1.33E-1334.37997352 41.45652723 34.37997352 41.45652723 Years of experience 0.622834743 0.114896219 5.420846294 5.66E-05 0.37926564 0.866403847 0.37926564 0.866403847 0.0450619860.025257854 1.784078159 0.093385-0.008482273 0.098606246 -0.008482273 0.098606246 1.38642789 3.925929911 0.001206 2.503922893 8.382114556 2.503922893 8.382114556 Coefficients Standard Error t Stat Intercept Principal's Rating Master's Degree 5.443018725

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(a) Step1: The null and alternati ve hypotheses are The slope coefficient is zero versus H1 At least one 0 (The slope coefficient is not equal to zero) b) Step 2 : The level of significance is α-005 Step3: The critical value of the F-test If F 2 3.238872. Reject Ho, otherwise do not reject H0 The critical value of F testis obtained by using the Excel2010 function FINV (0.05,3,16) 3.238872 Poas3u 3238872 Step4: The formula for calculating the test stati stic is The values of the Anova and the mulitple linear regressi on output of the Excel2010 is given below:MSR= 259.9726092, and MSE= 4.484229534 MSR MSE 259.972609:2 4.484229534 57.97487 F-57.97487 (c) Step5: The P-value approach P-value - P(F>57.97487) 1-P(F <57.97487) 1-0.999999992 0.0000000081 P-value0.00000000810.05. Wereject the null hypothesis Ho (d) Interpretation Step6: Since, the test statistic is F 57 97487> 053.16 3.238872 We reject the null hypothesis H There is sufficient evi dence to conclude that the independent variable (X) are significant predictors of the dependent variable (y) at the 5% level of significance We reject the null hypothesis Ho The fitted model is very useful to carry on the analysis of the given data.