At a recent county fair, you observed that at one stand people\'s weight was for

Question

At a recent county fair, you observed that at one stand people's weight was forecasted, and were surprised by the accuracy (within a range). Thinking about how the person could have predicted your weight fairly accurately (despite the fact that she did not know about your "heavy bones"), you think about how this could have been accomplished. You remember that medical charts for children contain 5%, 25%, 50%, 75% and 95% lines for a weight/height relationship and decide to conduct an experiment with 110 of your peers. You collect the data and calculate the following sums: where the height is measured in inches and weight in pounds. (a) Calculate the slope and intercept of the regression. (b) Find the regression R2.

Explanation / Answer

Yi = 17,375, X i = 7,665.5,

i=1 i=1

n n

yi2 = 94,228.8, xi2 = 1,248.9, xyii= 7,625.9

i=1 i=1 i=1

where the height is measured in inches and weight in pounds. (Small letters refer to deviations from means as in zZZ

a)

? ?

Answer: 1 ==6.11 , 0 =157.95 6.11×69.69 =267.86 . For every

1,248.9

additional inch in height, students weigh roughly 6 pounds more, on average.

b)

2 n

?

x2

2 ESS 1 i

Answer: R ==n i=1

TSS 2

yi

i=1

46,624.1

= =0.495 . Roughly half of the weight variation

94,228.8

in the 110 students is explained by the single explanatory variable, height. Answers will vary by student for the other factors, but calorie intake and amount of exercise typically appear as part of the list.

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