Question: The following data are measurements of tensile strength (100 lb/in2) and hardness (Rockwell E) on 20 pieces of die-cast aluminum
Suppose we consider the simple normal linear regression to describe the relationship between the response Y (strength) and the predictor X (hardness).
(a) Plot the data in a scatter plot.
(b) Calculate the least-squares line and plot this on the scatter plot in part (a).
(c) Plot the standardized residuals against X
(d) Produce a normal probability plot of the standardized residuals.
(e) What are your conclusions based on the plots produced in parts (c) and (d)?
(f) If appropriate, calculate 0.95-confidence intervals for the intercept and slope.
(g) Do the results of your analysis allow you to conclude that there is a relationship between Y and X? Explain why or why not.
(h) If the model is correct, what proportion of the observed variation in the response is explained by changes in the predictor?