Question

The head width (in) and weight (lb) is measured for a random sample of 20 bears. The data shows that the mean head width is 6.9 inches, mean weight is 214.3 lb, and the correlation r = 0.879 and its p-value is less than 0.0001. The suggested linear regression equation is WEIGHT = -212 + 61.9 WIDTH.

(a) How is the best predicted weight value of a given head width found with this data found?

(b) For the preceding part, why?

(c) Find the best predicted weight given a bear with a head with of 6.5 inches

Answer 1

A. The best predicted weight value of a given head width is found by putting the value of width in the following equation:
WEIGHT = -212 + 61.9 WIDTH

B. This is the linear regression equation which is calculated from the data using thr least squares method. And according to it the sum of squares of difference between the predicted value and true value is minimum. Hence it gives the least error and thus it gives the best predicted value.

C. The best predicted weight given a bear with a head with of 6.5 inches is:
Weight = -212 + 61.9×6.5 = 190.35 lb

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