The determination of the shear strength
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?
10 years ago
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- the_determination_of_the_shear_strength.xlsx