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
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 | 95 | 0 |
| 43.6 | 5 | 84 | 0 |
| 39.3 | 2 | 100 | 1 |
| 53 | 15 | 51 | 1 |
| 48.6 | 11 | 53 | 0 |
| 55 | 14 | 81 | 1 |
| 52 | 9 | 85 | 0 |
| 46.8 | 7 | 52 | 1 |
| 58.6 | 22 | 68 | 1 |
| 41.7 | 3 | 97 | 1 |
| 35.7 | 1 | 83 | 0 |
| 40.6 | 5 | 71 | 0 |
| 61.8 | 23 | 77 | 1 |
| 46.7 | 17 | 61 | 0 |
| 48.4 | 12 | 83 | 1 |
| 43.6 | 14 | 71 | 0 |
| 51.8 | 8 | 59 | 1 |
| 40.7 | 4 | 93 | 0 |
| 42.8 | 2 | 58 | 1 |
| 42.9 | 8 | 90 | 0 |
a. What is the question being asked?
b. Label your dependent variable: y =
c. Label your independent variables:
x1 =
x2 =
x3 =
d. Develop a
x1: r =
x2: r =
x3: r =
e. Compute and state the regression equation: (Round the intercept and the regression coefficients to 2 decimal places.)
ŷ = ______ + _______ x1 + ______ x2 + _______ x3
f. What salary would you estimate for a teacher with 6 years of experience, a rating by the principal of 71, and who has a master's degree? (Round to the nearest dollar)
Salary:
g. What does the value of the Coefficient of Determination tell you about the data?
h. Run a diagnosis to deterime if the model is significant at α = 0.01. (Round test statistic to 2 decimal places and p-value to 4 decimal places)
h1. Select the correct hypothesis statements.
H0:
H1:
h2. Test Statistic:
h3: p-value:
h4: What is your decision regarding the null hypothesis?
h5: What does this mean?
i. Run a diagnosis to determine if the slope of the individual variables are significant at α = 0.01. (Round p-values to 4 decimal places)
| Variable | p-value | Significant (Yes, No) |
| x1 | ||
| x2 | ||
| x3 |
j. Looking at the standared error of the regression model, what is the prediction
k. Is Multicollinearity a problem? Compute the VIF for each independent variable. (Round VIF to 3 decimal places)
| Variable | VIF | Problem (Yes, No) |
| x1 | ||
| x2 | ||
| x3 |
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?
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