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 Years Rating Masters 31.1 8 35 0 33.6 5 43 0 29.3 2 51 1 43 15 60 1 38.6 11 73 0 45 14 80 1 42 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
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.
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 | Years | Rating | Masters |
| 31.1 | 8 | 35 | 0 |
| 33.6 | 5 | 43 | 0 |
| 29.3 | 2 | 51 | 1 |
| 43 | 15 | 60 | 1 |
| 38.6 | 11 | 73 | 0 |
| 45 | 14 | 80 | 1 |
| 42 | 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 |
GIVEN:
| Subscriptions | Web Page Hits | Adv | Price | ||
| Subscriptions | 1 | ||||
| Web Page Hits | 0.642979 | 1 | |||
| Adv | 0.709228 | 0.357179 | 1 | ||
| Price | 0.710019 | 0.253957 | 0.441123 | 1 | |
| ŷ = | 19.915 | + | 0.899 | x1 + | 0.154 | x2 + | (0.667) | x3 |
| ŷ = | 33.647 | or | $33,647 |
FIND: the images below (the blanks)
Multiple linear regression model:
A multiple linear regression model is given as y = b0 + b1x1 + b2x2 + …+ bkxk where y is the predicted value of response variable, and x1, x2,…, xk are the k predictor variables. The quantities b1, b2,…, bk are the estimated slopes corresponding to x1, x2,…, xk respectively and b0 is the estimated intercept of the line, from the sample data.
A multiple regression equation describes the combined effect of all the predictors in the model. Even when the effect of a particular predictor is being studied from a multiple regression equation, it assumes that the effects of all the other predictors are accounted for.
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