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 β₀ = 300.00, β₁ = 1.085, and β₂ = 10.40. 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 α = 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 α = 0.05, what conclusions do you reach?