Chapter 10 10.2 a) The average score at age 35 for the people who scored 115 is estimated in the following way. First, the score of 115 is expressed in standard units (115 is 1 standard deviation above the mean, so it is 1.0 standard units above the mean). Second, the r-value describes to what degree the individuals' scores are constant over the years (how correlated the measures are). Multiplying r times the number of standard units gives: 1.0 * .8 s.u. = .8 s.u. Finally, converting back to an IQ score: .8 standard units = the mean + .8 * standard deviation, or... 100 + .8 * 15 = 112. b) The individual's score should be predicted to be 112. (see section 3) 10.3 a) around 64 inches. Same method as 10.2. b) around 62 inches. c) 63 inches. d) 63 inches. (when you don't have any info, predict the average value) 10.4 a) 15 years. Same method as 10.2. b) 13.5 years. c) Note that these are predicted results, so each prediction is accounting for the regression effect (section 5). 10.5 a) False. The correlation coefficient is not a proportion (except in unusual circumstances). b) False. R is a measure of correlation, but it does not imply any causal relationship. c) True. d) True. e) False. Again, r measures _correlation, not causation_. 10.7 Both doctors are probably wrong; this may be another example of the regression effect. 10.8 This data may provide evidence for the first doctor's argument, since the population _as a whole_, not just those people who had high readings, reduced in blood pressure. So, there may be two effects happening: the regression effect, which accounts for the fact that those people who had very low readings change to a higher reading, and an effect of relaxation, which explains the population-wide decrease in average reading. 10.10 False. This person's GPA is likely to change somewhat (due to the regression effect), so this persons GPA will likely be slightly higher. Chapter 11 11.2 Something is wrong. GPA's run from 0 to 4; if you predict 2, the maximum error is 2. The computer should be doing better than that. 11.3 a) sqrt[1-(0.8)^2] * 2.5 = 1.5 inches b) sqrt[1-(0.8)^2] * 1.7 = 1.0 inches 11.4 a) r.m.s. error = sqrt[1-r^2] * SD of final scores = 12 b) 65.8. This student is 30/25 = 1.2 SDs above average on the midterm, and should be above average on the final by r*1.2=0.72 SDs; that is, 10.8 points. c) 12, the r.m.s. error: see part a). It is OK to use the r.m.s. error inside a strip because the diagram is football- shaped. 11.5 a) The answer is about 5% P(score > 80) = P(z > 1.67) = Area to the right of 1.67 on st.norm.curve = 5 % b) New average = 65.8, new SD = 12, (80-65.8)/12 = 1.18 P(score > 80) = P(z > 1.18) = Area to the right of 1.18 on st.normal.curve = 12 % 11.6 No. The conclusion seems right, but does not follow from the data. It could be, for example, that better students spend more time doing homework anyway. 11.12 True, although the difference is pretty small. The correlation is negative; the men with 18 years of education should have blood pressures which are, on average, below the grand average by about 2 mm (by the regression method). In other words, the men with 18 years of education should have average blood pressures of about 122 mm. Chapter 12 12.2 Predicted income is ($960 per inch)*height - $37,400. Taller people make more money, on average. Probably, this reflects other variales in family background although looking every inch an executive probably doesn't hurt. 12.3 Obviously not. The slope means that the 141-pound men are taller, on average, than the 140-pound men - by around 0.047 inches. Similarly, the men who weigh 142 pounds are on average a little taller than the men who weigh 141 pounds, etc. 12.5 This is not legitimate. There are two regression lines; the one for predicting husbands from wives has slope 0.32. (see section 10.5) 12.6 The slope stays the same, and the intercept goes up by 10% 12.8 a) true b) false c) false d) true e) true (see Section 2)