Chapter 13, Problem 84PS

During the fall harvest season in the United States, pumpkins are sold in large quantities at farm stands. Often, instead of weighing the pumpkins prior to sale, the farm stand operator will just place the pumpkin in the appropriate circular cutout on the counter. When asked why this was done, one farmer replied, “I can tell the weight of the pumpkin from its circumference. “To determine whether this was really true, the circumference and weight of each from a sample of 23 pumpkins were determined and the results stored in Pumpkin.

a. Assuming a linear relationship, use the least-squares method to compute the regression coefficients $b_0$ and $b_1.$

b. Interpret the meaning of the slope, $b_1,$ in this problem.

c. Predict the mean weight for a pumpkin that is 60 centimeters in circumference.

d. Do you think it is a good idea for the farmer to sell pumpkins by circumference instead of weight? Explain.

e. Determine the coefficient of determination, $r^2,$ and interpret is meaning.

f. Perform a residual analysis for these data and evaluate the regression assumptions.

g. At the 0.05 of significance, is there evidence of a linear relationship between the circumference and weight of a pumpkin?

h. Construct a $95\%$ confidence interval estimate of the population slope, ${\beta }_1.$