1) You compare the height and weight of 5 adult women. You get the following results: height 60 67 62 70 66 weight 119 143 131 155 136 (a) Construct a scatter plot of height (x) vs. weight (y) (b) Calculate the following (show your work for SScp):
1) You compare the height and weight of 5 adult women. You get the following results:
height 60 67 62 70 66
weight 119 143 131 155 136
(a) Construct a scatter plot of height (x) vs. weight (y)
(b) Calculate the following (show your work for SScp):
SSx SSy SScp ̄x ̄y
(c) Calculate the
2) Use the information from problem 1. Perform a complete test of the hypothesis that the population
correlation coefficient (ρ) is 0. Show all steps (note - obviously this should be a one sided test! Make sure you
know why!).
3) Now let's assume you wanted to predict weights from heights. In other words, now let's use the same data
from problem (1) and do a regression instead.
(a) Calculate b0 and b1.
(b) Carefully draw your least square regression line on the plot you made in 1(a). (Don't just “sketch”,
be a little careful).
4) (a) Now do a significance test of H0: β1 = 0. Show all your calculations (including your residual
calculations). Again, note that this should be a one sided test (why?).
(b) Compare your t
*
from 4(a) with your t
*
from problem 2. Are they the same? This is not a coincidence,
although once you do more complicated analyses, you can't rely on this “equivalence”.
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