5 A student reports the following values from his bestfit li

5. A student reports the following values from his best-fit line: r = -.69, b = 1.45. Does this result make sense? Why or why not? (2 pt)

Below is a record of subjects IQs and the number of hours they spent watching cartoons this past year. Researchers are interested in if there is a relationship between the two variables. (8 pts)

Hours spent watching cartoons

38

139

217

219

106

41

0

IQ

171

123

88

92

165

167

209

Mean IQ = 145, Standard deviation of IQ = 45.09

Calculate the correlation coefficient (r) by hand. Show all steps to the calculation.

Describe the relationship between watching cartoons and IQ.

Solution

a) This result is contradictory. r = -0.69 means there is negative correlation between X and Y.i.e, if X increases, Y decreases. But b = 1.45 means Y increases 1.45 unit at unit increase in X which contradicts the previous result.

b) Mean IQ = 145, Sd(IQ) = 45.09

Mean Hours = 108.571

SD(Hours) = 81.256

mean(hours. IQ) = 12453.71

Cov(IQ, Hours) = 12453.71 - 145*108.571 = -3289.08

r = -3289.08/(45.09*81.256) = -0.898