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)Years of ExperiencePrincipal's Rating Master's Degree

Yx₁ x₂ x₃

31.1835 0

33.6 5 43 0

29.32511

43.015600

38.611730

45.014801

42.09760

36.87541

48.622551

31.73901

25.71300

30.65440

51.823841

46.717760

38.412681

33.614250

41.88 901

30.74620

32.82801

42.88720

a. 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.)

The correlation matrix is:

SalaryYearsRating

Years__________________

Rating__________________

Masters__________________

___________has the strongest correlation with salary. There ___________________to be a problem with multicollinearity.

b. 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:

= _________ + __________ x1 + _________ x2 + _________ x3

= _________ or _________

c. 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.)

HO is rejected if F >__________. Computed F = _____________ HO is _______________. At least one regression coefficient is not zero.

d. 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.)

A regression coefficient is dropped if computed t is to the left of _____________ or right of ____________

Keep" ___________ "and" __________"drop" ___________ ."

e. 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.)

Dropping" ___________, " we have : Salary = _____________+_____________(_____________) + ___________(_________)