The systolic blood pressure of individuals is thought to be related to both age and weight. For a random sample of 11 men, the following data were obtained:

(a) Generate summary statistics, including the mean and standard deviation of each variable compute the coefficient of variation for each variable. Relative to its mean, which variable has greatest spread of data values? Which variable has the smallest spread of data values relative to its mean?

(b) For each pair of variables, generate the sample correlation coeffi­cient r. Compute the corresponding coefficient of determination r₂. Which variable (other than x₁) has the greatest influence (by itself) on x₁? Would you say that both variables x₂ and x₃ show a strong influence on x₁ ? Explain your answer. What percent of the variation in x₁ can be explained by the corresponding variation in x₂ ? Answer the same question for x₃ .

(c) Perform a regression analysis with x₁ as the response variable. Use x₂ and x₃ as explanatory variables. Look at the coeffi­cient of multiple determination. What percentage of the variation in x₁ can be explained by the corresponding variations in x₂ and x₃ taken together?

(d) Look at the coeffi­cients of the regression equation. Write out the regression equation. Explain how each coeffi­cient can be thought of as a slope. If age were held ­fixed, but a person put on 10 pounds, what would you expect for the corresponding change in systolic blood pressure? If a person kept the same weight but got 10 years older, what would you expect for the corresponding change in systolic blood pressure?

(e) Test each coef­ficient to determine if it is zero or not zero. Use level of signifi­cance 5%. Why would the outcome of each test help us determine whether or not a given variable should be used in the regression model?

(f) Find a 90% con­fidence interval for each coef­ficient.

(g) Suppose Michael is 68 years old and weighs 192 pounds. Predict his systolic blood pressure, and fi­nd a 90% con­fidence range for your prediction (if your software produces prediction intervals).

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Systolic Age Weight Systolic Weight Blood Pressure (years) (pounds) Blood Pressure (years) (pounds) 132 143 153 162 154 168 52 59 67 173 184 194 211 196 220 137 149 159 128 166 54 61 65 46 72 188 188 207 167 217 64 74