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The following data are measurements of tensile strength (100 lb/in2) and hardness (Rockwell E) on…

The following data are measurements of tensile strength (100 lb/in2) and hardness (Rockwell E) on 20 pieces of die-cast aluminum

The following data are measurements of tensile strength (100 lb/in2) and hardness (Rockwell E) on...

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?