Amultiple 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 ˆ β0 = 300.00, ˆ β1 = 0.85, and ˆ β2 = 10.40. calculate an estimate of mean viscosity when x1 = 100of and x2 = 3 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 the f-statistic to assess the contribution of x3 to the model. using α = 0.05, what conclusion do you reach?