One general belief held by observers of the business world is that taller men earn more money than shorter men. In a study reported in the Wall Street Journal, 30 MBA graduates, all about 30 years old, were surveyed and asked to report their annual incomes and their heights. These responses are recorded in MBA.xlsx. a Estimate a linear relationship between heights and annual income of MBA graduates and interpret your results. b Do these data provide sufficient statistical evidence to infer at the 5% significance level that taller men with MBAs earn more money than shorter ones? c Provide a measure of the strength of the linear relationship between income and height. d Obtain three measures to check the fitness of the model. Do you think that this model is good enough to be used to estimate and predict income on the basis of height? If not, explain why not. If so, i predict the income of 183cm tall men with MBAs. ii estimate with 95% confidence the mean income of all 183 cm tall men with MBAs iii predict with 95% confidence the income of a 183 cm tall man with an MBA. Height Income ($)
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One general belief held by observers of the business world is that taller men earn more money than shorter men. In a study reported in the Wall Street Journal, 30 MBA graduates, all about 30 years old, were surveyed and asked to report their annual incomes and their heights. These responses are recorded in MBA.xlsx.
a Estimate a linear relationship between heights and annual income of MBA graduates and interpret your results.
b Do these data provide sufficient statistical evidence to infer at the 5% significance level that taller men with MBAs earn more money than shorter ones?
c Provide a measure of the strength of the linear relationship between income and height.
d Obtain three measures to check the fitness of the model. Do you think that this model is good enough to be used to estimate and predict income on the basis of height? If not, explain why not. If so,
i predict the income of 183cm tall men with MBAs.
ii estimate with 95% confidence the mean income of all 183 cm tall men with MBAs
iii predict with 95% confidence the income of a 183 cm tall man with an MBA.
| Height | Income ($) |
| 175.0 | 68660 |
| 167.5 | 74820 |
| 172.5 | 69260 |
| 175.0 | 79620 |
| 162.5 | 69180 |
| 182.5 | 66700 |
| 160.0 | 71140 |
| 175.0 | 83680 |
| 172.5 | 70060 |
| 182.5 | 77480 |
| 170.0 | 61340 |
| 165.0 | 61180 |
| 177.5 | 74740 |
| 170.0 | 78940 |
| 182.5 | 80540 |
| 182.5 | 75080 |
| 175.0 | 80980 |
| 177.5 | 75940 |
| 172.5 | 69640 |
| 182.5 | 74640 |
| 187.5 | 68120 |
| 170.0 | 65980 |
| 172.5 | 74060 |
| 190.0 | 72280 |
| 177.5 | 75840 |
| 165.0 | 67020 |
| 172.5 | 73520 |
| 162.5 | 67680 |
| 167.5 | 70720 |
| 175.0 | 80340 |
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