A sample of 716 adolescent girls from a particular health authority participated in a study of the relationship between systolic blood pressure (SBP) and resting heart rate (RHR). Measurements of SBP (in mm Hg) and RHR (in beats/min.) were taken on each girl. You may assume that the SBP measurements are independent and normally distributed with common SD. The data are available here: "RHR" "SBP"
73.9 166
77.6 166
97.2 188
80.9 172
81.5 167
99 182
85.2 177
66.2 150
72.5 162
75.2 165
93.6 185
84.1 174
84.5 171
81.3 174
74 170
99.8 192
85.6 167
58.5 153
87.8 177
74.9 166
68.4 160
77.7 167
68.8 158
72.1 165
73.2 165
61.5 155
89.3 188
81.8 174
67.6 158
1) Write down the linear regression model for these data. Be sure to define your variables and to state all assumptions.
2) Conduct the test of whether mean SBP is positively associated with RHR. In particular: Specify the null and alternative hypotheses, the value of the test statistic, the p-value and using a significance level of = 0.05, state your conclusions in the language of the problem.
3) Provide a 90% confidence interval for the mean SBP of girls with a RHR of 100 beats/min AND a 90% prediction interval for the SBP of a girl with a RHR of 100 beats/min.
4) Given an intuitive (not mathematical) explanation as to why your interval in (f) is so much wider than your interval in (e).