An automotive component manufacturer believes that the speed of the milling machine is related to the surface roughness in aluminum components. A random sample of aluminum components was obtained. Each piece had a 50350 mm cross section and was 100 mm in length. The speed of the milling machine (x, in rpm) and the surface roughness (y, in mm) was measured for each piece. MILLING
a. Find the estimated regression line and compute the residuals.
b. Carefully sketch a normal probability plot of the residuals and a plot of the residuals versus the predictor variable.
c. Do these graphs provide any evidence that the simple linear regression assumptions are invalid? Justify your answer.
Agriculture researchers recently investigated the relationship between wheat yield and wind speed. A random sample of wheat-field plots was obtained. The mean daily wind speed over the growing period (x, in m/s) was recorded for each field, along with the yield (y, in bushels per acre). The estimated regression line is y = 50.052 2 1.103x. WHEAT
a. Compute the residuals, and verify that they sum to 0.
b. Carefully sketch a graph of the residuals versus the predictor variable (wind speed). Is there any evidence that the simple linear regression assumptions are violated? Justify your answer.