A multiple regression model was used to relate y viscosity of a chemical product to x 1 temperature and x 2 reaction time The data set consisted of n 15 observations (a) The estimated regression coefficients were 0 300 00, 1 1 085, and 2 10 40 Calculate an estimate of mean viscosity when x 1 100 F and x 2 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, x 3 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 x 3 to the model Using 0 05, what conclusions do you reach

Question: A multiple regression model was used to relate y = viscosity of a chemical product to x 1 = temperature and x 2 = reaction

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?

(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?

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