Units of Measurement. A group of the U.S. scientist wants to learn the relations

Question

Units of Measurement. A group of the U.S. scientist wants to learn the relationship between individuals’ height and weight. In order to do this, a random sample of 200 twenty-year-old men is selected from a population and their height (measured in inches) and weight (measured in lbs) are recorded. A model relating weight to height is estimated: log(price) = 9.40 + 0.312 log(dist) (0.08) (0.020) weight = 99.41 + 3.94height n = 200,R2 = 0.81 (a) What is the predicted weight for someone who is 6 feet tall? 6’1” tall? 5’6” tall? 1 (b) A man has a late growth spur and grows 1.3” over a year. What is his predicted change in weight? (c) Interpret the R-squared of this regression. (d) Is there a meaningful interpretation for the intercept in this regression? Explain. (Hint: what is the predicted weight of someone with zero height? Someone who is only one inch high?) (e) A scientist in Germany is used to measuring height in centimeters and weight in kilograms, so instead of the pounds-inches regression results, she wants to see the kilograms-centimeters regression. Write down the regression estimates in terms of kilograms-centimeters relationship.

Explanation / Answer

a)

As

Weight = -99.41 + 3.94*height

Then if height = 72 in, then

Weight = -99.41 + 3.94*72 = 184.27 [ANSWER]

If height = 73 in, then

Weight = -99.41 + 3.94*73 = 188.21 [ANSWER]

If height = 66 in, then

Weight = -99.41 + 3.94*66 = 160.63 [ANSWER]

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b)

Change in weight = 3.94*change in height = 3.94*1.3 = 5.122

Hence, weight will increase by 5.122 lbs. [ANSWER]

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c)

It means 81% of the total variation in weight is explained by the height.

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d)

NO. We cannot have -99.41 lbs if your height is 0 inches.

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e)

Weight = -99.41 + 3.94*height

As 1 in = 2.54 cm, and 2.20462 lbs = 1 kg, then we divide the slope by 2.54, and divide it as well by 2.20462.

For the intercept, we simply divide it by 2.20462.

Hence,

Weight = -99.41/2.20462 + 3.94/(2.54*2.20462) height

Weight = -45.09167113 + 0.703604749 height [ANSWER]

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