11.6 The least-squares equation is

The male relationship has a lower intercept, but larger slope, with the lines crossing at a height of 60.2 inches and a weight of 121.6 pounds. Thus these equations predict that males shorter than 60.2 inches tend to weigh less than women of the same height, while males taller than 60.2 inches tend to be heavier than women of the same height.

Each equation has a negative weight at a zero height (x = -60); however, these equations are linear approximations that should not be used for unrealistic heights and weights.

11.8 a. The line was drawn so as to minimize the sum of squared vertical distances of the 22 points from the fitted line.
     b. The slope of the fitted line is positive, indicating (reasonably enough) that when the Democratic candidate wins big among the votes tabulated by voting machine, he or she also tends to win big among the votes tabulated by absentee ballot.
     c. This evidence was cited by the Republican because the 1993 election is an outlier: the absentee-ballot margin of victory is too large to be explained easily by the usual relationship between voting-machine and absentee-ballot results.

11.14 Division by the number of births and multiplication by 1,000 gives the late fetal and early neonatal death rates:

For late fetal deaths, here is a scatter diagram:

The least-squares regression (with the standard errors in parentheses and the t values in brackets) is

The least-squares line can be drawn in the scatter diagram by observing the predicted values of y for x = 20 and 50:

   The least-squares regression (with the standard errors in parentheses and the t values in brackets) is

There is a positive relationship, with the early-neonatal-deaths rate increasing with the mother's age. With 5 - 2 = 3 degrees of freedom; the observed 2.50 t value has a two-sided P value of 0.088. Thus the relationship is not statistically significant at the 5 percent level. To gauge whether the estimated effect is substantial, we can note that a ten-year increase in age from 33.3 (the mean) to 43.3 will increase the predicted level early-neonatal death rate by 0.94, which is 26 percent relative to the 3.61 mean. Again, the predicted number of deaths is small, about 0.472 + 0.094(43.3) = 4.6 per 1,000 births.
   Together, these data predict 10.6 late-fetal or early-neonatal deaths per 1,000 births for a 43.3 year old woman, which is roughly 26 percent higher than for a 33.3 year-old woman.

11.32 Here is a scatter diagram:

The least-squares estimated regression equation (with the standard errors in parentheses and the t values in brackets) is

The estimated slope is positive! However, the relationship is far from statistical significance, with an R-squared of virtually zero and a t value of only 0.64. With 25 - 2 degrees of freedom, P[t > 0.64] = 0.265, giving a two-sided P value of 2(0.265) = 0.53. Thus unlike the data for modern-day British women, these data show no evidence of a decrease in bone density between the ages of 15 and 45. (For women over the age of 45, the ancient and modern-day women both show a statistically significant decrease in bone density as they age, but the decrease is more rapid with modern day women.)

11.50 Here is a scatter diagram with the female data:

The least-squares estimated equation (with the standard errors in parentheses and the t values in brackets) is

The estimate of b is positive; however, its standard error is 0.14 and its t value is 0.85, giving a two-sided P value (with 15 - 2 = 13 degrees of freedom) of 0.41, which is far from statistically significant at the 5 percent level.
   Here is a scatter diagram and fitted line for the male running shoes:

The least-squares estimated equation is

The estimate of b is negative and almost statistically significant at the 5 percent level! Its t value is 1.28, giving a two-sided P value (with 15 - 2 = 13 degrees of freedom) of 0.075, which is not quite statistically significant at the 5 percent level.