Fuel Consumption and Cars
An automobile mechanic believes the weight of a tire is related to the overall diameter of the tire. A random sample of automobile tires was obtained and the diameter (x, inches) and weight (y, pounds) were measured for each. The estimated regression line was
y = 237.8316 + 2.46657x with n = 19, SSR = 87.1673, SSE = 258.8706, x = 25.3474, gx2i = 12221.6504, and Sxx = 14.3274.
a. Complete the ANOVA summary table, and conduct an F test for a significant regression. Explain the relationship between tire weight and tire diameter.
b. Find an estimate of the observed tire weight for a tire diameter of 25.2 inches.
c. Find a 99% prediction interval for an observed tire weight if the tire diameter is 24.8 inches.
d. Conduct the hypothesis test H0: β0 = 0 versus Ha: b0 ≠ 0 with significance level 0.01. Is there any evidence to suggest that the true regression line does not pass through the origin? Does this result make practical sense? Why or why not?