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?