According to the World Health Organization, obesity has reached epidemic proportions globally. While obesity has generally been linked with chronic disease and disability, researchers argue that it may also affect wages. In other words, the body mass index (BMI) of an employee is a predictor for salary. (A person is considered overweight if his/her BMI is at least 25 and obese if BMI exceeds 30.) The accompanying data file includes salary (in $1,000s) for 30 college-educated men with their respective BMI and a dummy variable that represents 1 for a white man and 0 otherwise. Salary BMI White 34 33 1 43 26 1 44 26 1 34 35 0 34 36 1 53 20 1 42 20 0 37 26 1 35 28 1 46 22 1 46 20 1 34 35 0 45 26 1 33 34 0 25 29 0 32 30 1 46 18 0 31 31 0 54 19 1 37 23 0 42 27 1 38 30 1 45 18 0 38 26 0 41 28 1 39 28 1 50 20 1 41 26 1 38 28 1 45 21 1 1. Estimate a model for Salary with BMI and White as the predictor variables. Note: Negative values should be indicated by a minus sign. Round your answers to 2 decimal places. 2. Reestimate the model with BMI, White, and a product of BMI and White as the predictor variables. Note: Negative values should be indicated by a minus sign. Round your answers to 2 decimal places. 3. Which of these models is the preferred model? A. Model 1, based on the R2 measure. B. Model 1, based on the adjusted R2 measure. C. Model 2, based on the R2 measure. D. Model 2, based on the adjusted R2 measure. 4. Use the preferred model to estimate the salary for a white college-educated man with a BMI of 30 and to compute the corresponding salary for a non-white man. Note: Round coefficient estimates to at least 4 decimal places and final answers to 2 decimal places.
According to the World Health Organization, obesity has reached epidemic proportions globally. While obesity has generally been linked with chronic disease and disability, researchers argue that it may also affect wages. In other words, the body mass index (BMI) of an employee is a predictor for salary. (A person is considered overweight if his/her BMI is at least 25 and obese if BMI exceeds 30.) The accompanying data file includes salary (in $1,000s) for 30 college-educated men with their respective BMI and a dummy variable that represents 1 for a white man and 0 otherwise.
| Salary | BMI | White |
| 34 | 33 | 1 |
| 43 | 26 | 1 |
| 44 | 26 | 1 |
| 34 | 35 | 0 |
| 34 | 36 | 1 |
| 53 | 20 | 1 |
| 42 | 20 | 0 |
| 37 | 26 | 1 |
| 35 | 28 | 1 |
| 46 | 22 | 1 |
| 46 | 20 | 1 |
| 34 | 35 | 0 |
| 45 | 26 | 1 |
| 33 | 34 | 0 |
| 25 | 29 | 0 |
| 32 | 30 | 1 |
| 46 | 18 | 0 |
| 31 | 31 | 0 |
| 54 | 19 | 1 |
| 37 | 23 | 0 |
| 42 | 27 | 1 |
| 38 | 30 | 1 |
| 45 | 18 | 0 |
| 38 | 26 | 0 |
| 41 | 28 | 1 |
| 39 | 28 | 1 |
| 50 | 20 | 1 |
| 41 | 26 | 1 |
| 38 | 28 | 1 |
| 45 | 21 | 1 |
1. Estimate a model for Salary with BMI and White as the predictor variables.
Note: Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.
2. Reestimate the model with BMI, White, and a product of BMI and White as the predictor variables.
Note: Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.
3. Which of these models is the preferred model?
4. Use the preferred model to estimate the salary for a white college-educated man with a BMI of 30 and to compute the corresponding salary for a non-white man.
Note: Round coefficient estimates to at least 4 decimal places and final answers to 2 decimal places.
From the given data we have,
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