Chapter 9.4, Problem 3P

For Problems 3-6, use appropriate multiple regression software of your choice and enter the data. Note that the data are also available for download at the Companion Sites for this text.

3. Medical: Blood Pressure 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:

1. (a) Generate summary statistics, including the mean and standard deviation of each variable. Compute the coefficient of variation (see Section 3.2) for each variable. Relative to its mean, which variable has the greatest spread of data values? Which variable has the smallest spread of data values relative to its mean?
2. (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.
3. (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 x₃ and x₃ taken together?
4. (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?
5. (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?
6. (f) Find a 90% confidence interval for each coefficient.
7. (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).