The determination of the shear strength of spot welds is relatively difficult, whereas measuring the weld diameter of spot welds is relatively simple. As a result, it would be advantageous if shear strength could be predicted from a measurement of weld diameter. The data are as follows:
(a) Draw a scatter diagram.
(b) Find the least squares estimates of the regression coefficients.
|
Shear Strength (psi)
|
Weld Diameter (.0001 in.
|
|
370
|
400
|
|
780
|
800
|
|
1,210
|
1,250
|
|
1,560
|
1,600
|
|
1,980
|
2,000
|
|
2,450
|
2,500
|
|
3,070
|
3,100
|
|
3,550
|
3,600
|
|
3,940
|
4,000
|
|
3,950
|
4,000
|
(c) Test the hypothesis that the slope of the regression line is equal to 1 at the.05 level significance.
(d) Estimate the expected value of shear strength when the weld diameter is .2500.
(e) Find a prediction interval such that, with 95 percent confidence, the value of shear strength corresponding to a weld diameter of .2250 inch will be contained in it.
(f) Plot the standardized residuals.
(g) Does the plot in part (f) support the assumptions of the model?