It would still be 0.36. Correlation does not change when the units of measurement change.
Problem 3.
a) y = 0.96(x - 0.5) = -0.48 + 0.96 x (in pints)
b) The intercept is -0.48 and doesn't have any physical meaning. It would be the volume of water corresponding to a weight of 0, but zero is not a possible value since the container weighs 0.5 lbs. The slope is 0.96 and represents the additional volume of water (in pints) when the weight is increased by 1 lb.
c) This is a deterministic relationship, not a statistical relationship, so the correlation is one.
Problem 5.
The sample size of 10,000 is more likely. Even a minor relationship will achieve statistical significance if the sample is very large. Problem 9.
Correlation measures only how closely the points fall to a straight line. A perfect curved relationship where the best line through the points is flat would have a zero correlation. For example x versus x^2 for x = -3, -2, -1, 0, 1, 2, 3.
Problem 10.
a) Predicted GPA = 0.539 + (.00362)*(500) = 2.349
b) For each increase of 1 in verbal SAT score we would expect to see an increase of 0.00362 in GPA.
c) No. It would be the GPA for someone with an SAT score of 0, but that's not a possible score for the SAT.
Problem 11.
a) Man 157.5 lbs, woman 133.9 lbs. Men who weigh 150 pounds would ideally like to weigh slightly more, while women who weigh 150 lbs would like to weigh much less.
b) No, it would be the ideal weight for a women whose actual weight was 0, which is obviously meaningless.
c) Yes, the slope of 0.6 indicates that on average, for two women whose actual weight differs by one pound, their ideal weights differ by 0.6 lbs.
d) Someone whose weight is in the normal range, but who wants to weigh much less or more than they do, so much that they don;t fit the pattern for their sex. For example, there is a woman whose actual weight is 105 pounds, but who would like to weigh 125 pounds. In the other direction is a woman who weighs 140 pounds but would like to weigh 100 pounds, much more of a discrepancy than the majority of women.