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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
(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?
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