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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 coeffi cient 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 coeffi cient 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 coeffi cients of the regression equation. Write out the regression equation. Explain how each coeffi cient 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 b |
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