You Are at a College of Roughly 1,000 Students and Obtain

Essay

You are at a college of roughly 1,000 students and obtain data from the entire freshman class (250 students)on height and weight during orientation. You consider this to be a population that you want to describe, rather than a sample from which you want to infer general relationships in a larger population. Weight (Y)is measured in pounds and height (X)is measured in inches. You calculate the following sums: $\sum _ { i = 1 } ^ { n } y _ { i } ^ { 2 }$ = 94,228.8, $\sum _ { i = 1 } ^ { n } x _ { i } ^ { 2 }$ = 1,248.9, $\sum _ { i = 1 } ^ { n } x _ { i } y _ { i }$ = 7,625.9
(small letters refer to deviations from means as in $\mathrm { z } _ { i }$ = $Z _ { i }$ - $\bar { Z }$ ).
(a)Given your general knowledge about human height and weight of a given age, what can you say about the shape of the two distributions?
(b)What is the correlation coefficient between height and weight here?