A study was conducted on automobile engines to examine the relationship between engine speed measured in revolutions per minute (RPM) and engine torque with the goal of predicting engine torque. (Data extracted from Y. Chen et al., "Cluster-Based Profile Analysis in Phase I," Journal of Quality Technology, 47, January 2015, and stored in Engines.)

a. Construct a scatter plot for RPM and torque.

b. Fit a quadratic regression model and state the quadratic regression equation.

c. Predict the mean torque for an RPM of 3,000.

d. Perform a residual analysis on the results and determine whether the regression assumptions are valid.

e. At the 0.05 level of significance, is there a significant quadratic relationship between torque and RPM?

f. At the 0.05 level of significance, determine whether the quadratic model is a better fit than the linear model.

g. Interpret the meaning of the coefficient of multiple determination.

h. Compute the adjusted r2.

i. What conclusions can you reach concerning the relationship between RPM and torque?