The article An Experimental Study of Resistance Spot Welding in 1 mm Thick Sheet of Low Carbon

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The article “An Experimental Study of Resistance Spot Welding in 1 mm Thick Sheet of Low Carbon Steel” (J. of Engr. Manufacture, 1996: 341–348) discussed a statistical analysis whose basic aim was to establish a relationship that could explain the variation in weld strength (y) by relating strength to the process characteristics weld current (wc), weld time (wt), and electrode force (ef).

a. SST  16.18555, and fitting the complete second-order model gave SSE  .80017. Calculate and interpret the coefficient of multiple determination.

b. Assuming that n  37, carry out a test of model utility (the ANOVA table in the article states that n  (k 1)  1, but other information given contradicts this and is consistent with the sample size we suggest).

c. The given F ratio for the current–time interaction was 2.32. If all other predictors are retained in the model, can this interaction predictor be eliminated? [Hint: As in simple linear regression, an F ratio for a coefficient is the square of its t-ratio.]

d. The authors proposed eliminating two interaction predictors and a quadratic predictor and recommended the estimated equation y  3.352 .098wc .222wt

.297ef  .0102(wt)2  .037(ef)2 .0128(wc)(wt).

Consider a weld current of 10 kA, a weld time of 12 ac cycles, and an electrode force of 6 kN. Supposing that the estimated standard deviation of the predicted strength in this situation is .0750, calculate a 95% PI for strength.

Does the interval suggest that the value of strength can be accurately predicted?

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