5. A student reports the following values from his best-fit line: r = -.69, b =
ID: 3386803 • Letter: 5
Question
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.
Hours spent watching cartoons
38
139
217
219
106
41
0
IQ
171
123
88
92
165
167
209
Explanation / Answer
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
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