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).
  

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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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 consis- tent 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 sim- ple linear regression, an F ratio for a coefficient is the square of its t ratio.] d. The authors proposed eliminating two interaction pre- dictors and a quadratic predictor and recommended the estimated equation y = 3.352 + .098wc + .222wt + .297ef – .0102(wt)? – .037(ef)? + .0128(wc)(wt). 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 consis- tent 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 sim- ple linear regression, an F ratio for a coefficient is the square of its t ratio.] d. The authors proposed eliminating two interaction pre- dictors and a quadratic predictor and recommended the estimated equation y = 3.352 + .098wc + .222wt + .297ef – .0102(wt)? – .037(ef)? + .0128(wc)(wt).