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 a = 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 a = 0.05, what conclusions do you reach?