A multiple regression model was used to relate y viscosity of a chemical product to x1 temperature and x2 reaction time. The data set consisted of n 15 observations.

(a) The estimated regression coefficients were and . Calculate an estimate of mean viscosity when x1 100°F and x2 2 hours.

(b) The sums of squares were SST 1230.50 and SSE 120.30. Test for significance of regression using 0.05. What conclusion can you draw?

(c) What proportion of total variability in viscosity is accounted for by the variables in this model?

(d) Suppose that another regressor, x3 stirring rate, is added to the model. The new value of the error sum of squares is SSE 117.20. Has adding the new variable resulted in a smaller value of MSE? Discuss the significance of this result.

(e) Calculate an F-statistic to assess the contribution of x3 to the model. Using 0.05, what conclusions do you reach?