Problem 14] Pace of Life and Heart Disease. Some believe that individuals with a constant sense of time urgency (often called type-A behavior) are more susceptible to heart disease than are more relaxed individuals. Although most studies of this issue have focused on individuals, some psychologists have investigated geographical areas. They considered the relationship of city-wide heart disease rates and general measures of the pace of life in the city. For each region of the United States (Northeast, Midwest, South, and West) they selected three large metropolitan areas, three medium-size cities, and three smaller cities. In each city they measured three indicators of the pace of life.

The variable walk is the walking speed of pedestrians over a distance of 60 feet during business hours on a clear summer day along a main downtown street. Bank is the average time a sample of bank clerks takes to make change for two $20 bills or to give $20 bills for change. The variable talk was obtained by recording responses of postal clerks explaining the difference between regular, certified, and insured mail and by dividing the total number of syllables by the time of their response. The researchers also obtained the age-adjusted death rates from ischemic heart disease (a decreased flow of blood to the heart) for each city (heart). The data in Display 9.17 were read from a graph in the published paper. (Data from R. V. Levine, The Pace of Life, American Scientist 78 (1990): 450 9.) The variables have been standardized, so there are no units of measurement involved.

(a)Draw a matrix of scatterplots of the four variables. Construct it so that the bottom row of plots all have heart on the vertical axis. If you do not have this facility, draw scatterplots of heart versus each of the other variables individually.

(b)Obtain the least squares fit (estimated coefficients) to the linear regression of heart (response) on bank, walk, and talk.

(c)Plot the residuals versus fitted values. Is there evidence that the variance of the residual increases with increasing fitted values or that there are any outliers?

(d)Report a summary of the least squares fit. Write down the estimated equation with standard errors below each estimated coefficient. (This is a professional way to write down the fitted regression line. )