Mike Wilde is president of the teachers’ union for Otsego School District. In preparing for upcoming negotiations, he is investigating 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 teaching effectiveness rating 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 ($ thousands), y Years of Experience, x1 Principal's Rating, x2 Master's Degree,* x3 31.1 8 35 0 33.6 5 43 0 29.3 2 51 1 43.0 15 60 1 38.6 11 73 0 45.0 14 80 1 42.0 9 76 0 36.8 7 54 1 48.6 22 55 1 31.7 3 90 1 25.7 1 30 0 30.6 5 44 0 51.8 23 84 1 46.7 17 76 0 38.4 12 68 1 33.6 14 25 0 41.8 8 90 1 30.7 4 62 0 32.8 2 80 1 42.8 8 72 0 *1 = yes, 0 = no. Click here for the Excel Data File Develop a correlation matrix. Which independent variable has the strongest correlation with the dependent variable? Does it appear there will be any problems with multicollinearity? (Round your answers to 3 decimal places.) Determine the regression equation. What salary would you estimate for a teacher with 5 years’ experience, a rating by the principal of 60, and no master’s degree? (Negative amount should be indicated by a minus sign. Round salary to nearest whole number, all other answers to 3 decimal places.) The regression equation is: Conduct a global test of hypothesis to determine whether any of the regression coefficients differ from zero. Use the 0.05 significance level. (Round your answers to 2 decimal places.) Conduct a test of hypothesis for the individual regression coefficients. Would you consider deleting any of the independent variables? Use the 0.05 significance level. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

Mike Wilde is president of the teachers’ union for Otsego School District. In preparing for upcoming negotiations, he is investigating 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 teaching effectiveness rating 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 ($ thousands), y Years of Experience, x1 Principal's Rating, x2 Master's Degree,* x3 31.1 8 35 0 33.6 5 43 0 29.3 2 51 1 43.0 15 60 1 38.6 11 73 0 45.0 14 80 1 42.0 9 76 0 36.8 7 54 1 48.6 22 55 1 31.7 3 90 1 25.7 1 30 0 30.6 5 44 0 51.8 23 84 1 46.7 17 76 0 38.4 12 68 1 33.6 14 25 0 41.8 8 90 1 30.7 4 62 0 32.8 2 80 1 42.8 8 72 0 *1 = yes, 0 = no. Click here for the Excel Data File Develop a correlation matrix. Which independent variable has the strongest correlation with the dependent variable? Does it appear there will be any problems with multicollinearity? (Round your answers to 3 decimal places.) Determine the regression equation. What salary would you estimate for a teacher with 5 years’ experience, a rating by the principal of 60, and no master’s degree? (Negative amount should be indicated by a minus sign. Round salary to nearest whole number, all other answers to 3 decimal places.) The regression equation is: Conduct a global test of hypothesis to determine whether any of the regression coefficients differ from zero. Use the 0.05 significance level. (Round your answers to 2 decimal places.) Conduct a test of hypothesis for the individual regression coefficients. Would you consider deleting any of the independent variables? Use the 0.05 significance level. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

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Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 10CYU

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Salary ($ thousands), y	Years of Experience, x₁	Principal's Rating, x₂	Master's Degree,* x₃
31.1		8		35	0
33.6		5		43	0
29.3		2		51	1
43.0		15		60	1
38.6		11		73	0
45.0		14		80	1
42.0		9		76	0
36.8		7		54	1
48.6		22		55	1
31.7		3		90	1
25.7		1		30	0
30.6		5		44	0
51.8		23		84	1
46.7		17		76	0
38.4		12		68	1
33.6		14		25	0
41.8		8		90	1
30.7		4		62	0
32.8		2		80	1
42.8		8		72	0

^*1 = yes, 0 = no.

Click here for the Excel Data File

Develop a correlation matrix. Which independent variable has the strongest correlation with the dependent variable? Does it appear there will be any problems with multicollinearity? (Round your answers to 3 decimal places.)

Determine the regression equation. What salary would you estimate for a teacher with 5 years’ experience, a rating by the principal of 60, and no master’s degree? (Negative amount should be indicated by a minus sign. Round salary to nearest whole number, all other answers to 3 decimal places.)

The regression equation is:

Conduct a global test of hypothesis to determine whether any of the regression coefficients differ from zero. Use the 0.05 significance level. (Round your answers to 2 decimal places.)

Conduct a test of hypothesis for the individual regression coefficients. Would you consider deleting any of the independent variables? Use the 0.05 significance level. (Negative amounts should be indicated by a minus sign. Round your answers to 3 decimal places.)

If your conclusion in part (d) was to delete one or more independent variables, run the analysis again without those variables. (Round your answers to 4 decimal places.)

State true or false.

From the graph the residuals appear normally distributed.

multiple choice 1

True
False

Choose the right option from the following graph.

multiple choice 2

The residuals look random.
The residuals do not look random.

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