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MATH 2565 (19)


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York University
Mathematics and Statistics
MATH 2565
Jagmohan Chawla

Problem 7.15: Lunchtime. a) The correlation between time toddlers spent at the table and the number of calories consumed by the toddlers is r = –0.649. b) If time spent at the table were recorded in hours instead of minutes, the correlation would not change at all. Correlation is calculated from z-scores, and since these unitless measures of position are unaffected by changes in scale, correlation is likewise unaffected. c) The correlation between time spent at the table and calorie consumption for toddlers is –0.649, a moderate, negative correlation. Toddlers who spent more time at the table tended to consume fewer calories. d) The analyst’s remark is speculative. There are many possible explanations for the behaviour of the toddlers. The data merely show us an association between time spent at the table and calories consumed by toddlers, and association is not the same thing as a cause-and- effect relationship. . Problem7.33 Thrills. The scatterplot at the right shows that the association between Drop and Duration is straight, positive, and weak, with no outliers. Generally, rides on coasters with a greater initial drop tend to last somewhat longer. The correlation between Drop and Duration is 0.35, indicating a weak association. Problem 8.1: Regression equations. x sx y a) 10 2 20 b) 2 0.06 7.2 1.2 c) 12 6 152 30 d) 2.5 1.2 25 100 a) rs b1= y y = 0 + 1 x sx y = b0+ b1x (0.5)(3) 20= b + 0.75(10) b1= 2 0 b0= 12.5 b1= 0.75 y = b + b x 0 1 y = 0 + 1 x
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