Question
Please use Python code to find the following answers. One may wonder if people of similar heights tend to marry each other. For this purpose,
Please use Python code to find the following answers.
One may wonder if people of similar heights tend to marry each other. For this purpose, a sample of newly married couples was selected. Let be the height of the husband and be the height of the wife. The heights (in cm) of husbands and wives are found in below table.
| HH | WH |
| 186 | 175 |
| 180 | 168 |
| 160 | 154 |
| 186 | 166 |
| 163 | 162 |
| 172 | 152 |
| 192 | 179 |
| 170 | 163 |
| 174 | 172 |
| 191 | 170 |
| 182 | 170 |
| 178 | 147 |
| 181 | 165 |
| 168 | 162 |
| 162 | 154 |
| 188 | 166 |
| 168 | 167 |
| 183 | 174 |
| 188 | 173 |
| 166 | 164 |
| 180 | 163 |
| 176 | 163 |
| 185 | 171 |
| 169 | 161 |
| 182 | 167 |
| 162 | 160 |
| 169 | 165 |
| 176 | 167 |
| 180 | 175 |
| 157 | 157 |
| 170 | 172 |
| 186 | 181 |
| 180 | 166 |
| 188 | 181 |
| 153 | 148 |
| 179 | 169 |
| 175 | 170 |
| 165 | 157 |
| 156 | 162 |
| 185 | 174 |
| 172 | 168 |
| 166 | 162 |
| 179 | 159 |
| 181 | 155 |
| 176 | 171 |
| 170 | 159 |
| 165 | 164 |
| 183 | 175 |
| 162 | 156 |
| 192 | 180 |
| 185 | 167 |
| 163 | 157 |
| 185 | 167 |
| 170 | 157 |
| 176 | 168 |
| 176 | 167 |
| 160 | 145 |
| 167 | 156 |
| 157 | 153 |
| 180 | 162 |
| 172 | 156 |
| 184 | 174 |
| 185 | 160 |
| 165 | 152 |
| 181 | 175 |
| 170 | 169 |
| 161 | 149 |
| 188 | 176 |
| 181 | 165 |
| 156 | 143 |
| 161 | 158 |
| 152 | 141 |
| 179 | 160 |
| 170 | 149 |
| 170 | 160 |
| 165 | 148 |
| 165 | 154 |
| 169 | 171 |
| 171 | 165 |
| 192 | 175 |
| 176 | 161 |
| 168 | 162 |
| 169 | 162 |
| 184 | 176 |
| 171 | 160 |
| 161 | 158 |
| 185 | 175 |
| 184 | 174 |
| 179 | 168 |
| 184 | 177 |
| 175 | 158 |
| 173 | 161 |
| 164 | 146 |
| 181 | 168 |
| 187 | 178 |
| 181 | 170 |
1. Compute the covariance between the heights of the husbands and wives.
2. What would the covariance be if heights were measured in inches rather than in cm?
3. Compute the correlation coefficient between the heights of the husband and wife.
4. What would the correlation be if heights were measured in inches rather than in cm?
5. What would the correlation be if every man married a woman exactly 5 cm shorter than him? 6. We wish to fit a regression model relating the heights of husbands and wives. Which one of the two variables would you choose as the response variable? Justify your answer.
7. Give a scatter plot of the response variable versus the predictor variable.
8. Using your choice of the response variable in (5.), test the null hypothesis that the slope is zero.
9. Using your choice of the response variable in (5.), test the null hypothesis that the intercept is zero. (k) Give comments on the normality of the residuals.
11. Refit the regression after removing the outlier(s). Compare the two regression lines.
12. Check the normality of the residuals of the last regression (the one with outliers removed). What is your comment?
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Practical Linear Algebra A Geometry Toolbox
Authors: Gerald Farin, Dianne Hansford
3rd Edition
1466579587, 9781466579583
