Exercise 1 (18 marks) The following table presents shear strengths (in kN/mm) and weld diameters (in mm) for a sample of spot welds. Strength 51 Diameter 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8 468024600 54 69 81 75 79 89 101 6.0 98 102 a) Construct a scatterplot of strength (y) versus diameter (x). Verify that a linear model is appropriate. (done by hand) b) Compute the least-squares line for predicting strength from diameter. (show all your calculations) Compute the fitted values (i.e. the predicted values) and the residual for each point. Which point has the residual with the largest magnitude? (can be done in excel) d) If the diameter is increased by 0.3 mm, by how much would you predict the strength to increase or decrease? e) Predict the strength for a diameter of 5.5 mm. f) Can the least-squares line be used to predict the strength for a diameter of 8mm? If so, predict the strength. If not, explain why not. g) For what diameter would you predict a strength of 95 kN/mm? h) Compute the regression sum of squares, the error sum of squares, and the total sum of squares. i) Divide the regression sum of squares by the total sum of squares. What is the relationship between this quantity and the correlation coefficient?