a. Determine the regression equation. What salary would you estimate for a teacher with 11 years of experience, a rating by the principal of 55, and no master’s degree? (answer in 2 decimal places) b. How much does an additional of 2 years of experience add to the salary amount? (answer in 2 decimal places) c. What is the value of coefficient of determination? (answer in 3 decimal places)
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
A president of the teachers’ union is preparing for upcoming negotiations. He is investigating the salary structure of classroom teachers in a 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 (0 = no, 1 = yes). A random sample of 20 teachers resulted in the following data.
| Salary | Years | Rating | Masters |
| 31.100 | 8 | 35 | 0 |
| 33.600 | 5 | 43 | 0 |
| 29.300 | 2 | 51 | 1 |
| 43.000 | 15 | 60 | 1 |
| 38.600 | 11 | 73 | 0 |
| 45.000 | 14 | 80 | 1 |
| 42.000 | 9 | 76 | 0 |
| 36.800 | 7 | 54 | 1 |
| 48.600 | 22 | 55 | 1 |
| 31.700 | 3 | 90 | 1 |
| 25.700 | 1 | 30 | 0 |
| 30.600 | 5 | 44 | 0 |
| 51.800 | 23 | 84 | 1 |
| 46.700 | 17 | 76 | 0 |
| 38.400 | 12 | 68 | 1 |
| 33.600 | 14 | 25 | 0 |
| 41.800 | 8 | 90 | 1 |
| 30.700 | 4 | 62 | 0 |
| 32.800 | 2 | 80 | 1 |
| 42.800 | 8 | 72 | 0 |
a. Determine the regression equation. What salary would you estimate for a teacher with 11 years of experience, a rating by the principal of 55, and no master’s degree? (answer in 2 decimal places)
b. How much does an additional of 2 years of experience add to the salary amount? (answer in 2 decimal places)
c. What is the value of coefficient of determination? (answer in 3 decimal places)
d. What percent of variation is not explained? (answer in 2 decimal places; no need to write the percentage)
Conduct a global test of hypothesis to see if any of the set of regression coefficients could be different from 0. Use the 0.05 significance level.
e. What is the value of test statistics? (answer in 3 decimal places)
f. If your conclusion in part (g) was to delete one or more independent variables, run the analysis again without those variables. What is the value of Adjusted coefficient of determination? (answer in 3 decimal places)
Notes: if your answer in part (g) was not to delete any variables, then answer this question with zero (0).
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