Thus far we have constructed linear models for data that represent a function of some independent variable. Frequently in the “real world,” we are confronted with a set of data that does not actually describe a function, but that suggests an underlying relationship that might be modeled by a function. An example of such data is the relationship between height and weight for the seven infielders on the Los Angeles Dodgers roster on July 12, 1997.
Height in inches h | 70 | 74 | 71 | 71 | 76 | 70 | 73 |
Weight in pounds W | 163 | 170 | 180 | 145 | 222 | 185 | 200 |
a. Find the linear model that best fits these data.
b. Use the linear model to predict the weight of a major league infielder who is 6 feet tall.
c. Should you use this model to predict the weight of any American male who is 6 feet tall? Why or why not?
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