Does your age and weight affect your blood pressure? To test this, a medical researcher collected measures of systolic blood pressure (in \(\mathrm{mmHg}\), millimeters of mercury), age (in years), and weight (in pounds) for a random sample of 17 individuals. These measures are presented in Table 8.7.

a. Write the population linear regression equation.

b. Using this data set, develop a model that can be used to predict systolic blood pressure based on age and weight.

c. Draw a matrix plot that shows the relationship between the response and each of the predictor variables.

d. Is the overall model useful in predicting systolic blood pressure?

e. Use exploratory techniques and any formal tests to check relevant model assumptions and check for multicollinearity.

f. What factors are significant in predicting systolic blood pressure? Interpret your findings in the context of the problem and comment on whether you think your conclusions make sense.
g. Using your estimated regression equation, estimate what the average systolic blood pressure would be for an individual who is 35 years old and weighs 154 pounds.

h. Can you think of any other factors that could impact systolic blood pressure?

Table 8.7

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Systolic Blood Pressure, Age, and Weight for a Random Sample of 17 Individuals Systolic Blood Pressure (mmHg) Age (in Years) Weight (in Pounds) 128 58 190 136 63 171 141 74 139 134 68 186 123 47 187 128 50 182 141 58 176 124 53 137 140 37 154 121 29 185 124 132 49 34 158 180 134 47 145 145 58 184 122 28 145 119 23 158 119 20 159