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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 X be the height of the husband and Y be the height of the wife. The heights (in centimeters) of husbands and wives are found in Table 2.11. The data can also be found at the book's Website. (a) Compute the covariance between the heights of the husbands and wives. (b) What would the covariance be if heights were measured in inches rather than in centimeters?
Row W 1 2 175 169 149 3 4 176 5 6 7 166 143 158 141 8 9 10 12 13 心以四四四四四。 14 15 16 Table 211 Heights of Husband (H) and Wife (W) m (Centimeters) H Row H W Row H 186 175 33 180 166 65 181 180 168 34 188 181 66 170 160 154 35 153 148 161 186 166 36 179 169 68 188 163 162 37 175 170 69 181 172 152 38 165 IS7 TO 156 192 179 39 156 162 71 161 170 163 40 185 174 72 152 174 172 41 172 168 73 179 191 170 166 162 74 170 182 170 43 179 159 75 170 178 147 44 181 155 776 166 181 165 45 176 77 165 168 162 46 170 159 78 169 154 47 165 164 171 188 166 48 183 175 80 192 168 167 49 162 156 176 183 174 50 192 180 82 168 188 173 51 185 167 83 169 166 164 52 16B 157 84 184 180 163 53 185 167 85 171 176 163 54 170 IST 86 161 185 55 176 168 87 185 169 161 56 176 167 88 184 182 167 S7 160 145 89 162 160 58 167 156 90 184 169 165 59 157 183 91 178 176 167 60 180 162 92 173 180 175 61 172 156 93 157 157 184 174 94 181 170 172 63 185 160 95 IR 186 BI 165 192 181 19 162 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 160 149 160 148 154 171 165 175 161 162 162 176 160 158 175 174 168 17" 158 161 179 168 178 TO 04 96
(c) Compute the comelation coefficient between the heights of the husband and wife, (d) What would the conrelation be if heights were measured in inches rather than in centimeters? (e) What would the correlation be if every man married a woman exactly 5 centimeters shorter than him? (f) 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. (@) Using your choice of the response variable in Exercise 2.10(0). test the null hypothesis that the slope is zero. (h) Using your choice of the response variable in 2.10(6), test the null hypoth- esis that the intercept is zero.