You work for a high-volume bakery and have been asked to develop a statistical model to predict and assess the quality of the bread product as it relates to the time and temperature of the manufacturing (baking) process. You have collected time temperature experimental data shown in the attached "BreadExp" data file. You have also noted the weather on the days the bread was baked with a 0-1 indicator variable. (0= Cool and dry, 1= Warm and wet). The response is a quality score metric called QScore.

1.[10 Points] Write the complete second order model with interaction that uses temperature and time as the explanatory variables.

2.[10 Points] Fit the regression equation for the model in Part 1 and submit the complete Minitab output. Include the sequential sums of squares in the output submitted.

3.[10 Points]

(a)Construct a well-designed plot of the model-predicted values for the response (on Y-axis) as a function of the baking temperature (on x-axis) for baking times of 37, 35 and 33 minutes. (Points on the plot for each baking time should be connected with lines.)

(b)Construct a well-designed plot of the model-predicted values for the response (on Y-axis) as a function of the baking time (on x-axis) for baking temperatures of 340, 350, 360 degrees F. (Points on the plot for each baking temperature should be connected with lines.)

4.[20 Points] Construct a well-designed plot with the observed QScore on the Y-axis and the predicted values from the fitted model in Question 2 on the x-axis. On this plot, include a fitted simple regression line and the associated 95 % confidence and prediction limit lines. Also, submit the complete Minitab regression analysis output for this part.

5.[15 Points] Add to the regression model of Question 2 the weather categorical predictor variable. Submit the associated Minitab output. Does the weather statistically affect the QScore for a 95% level of significance? Clearly justify your answer.

6.[15 Points]

(a)What is the value of R² from the analysis in Question 2? Interpret in practical terms.

(b)What is the value of the R² value from the analysis in Question 5? Interpret in practical terms.

(c)How are the two R² values in (a) and (b) above related? Is this what you would expect? Clearly explain why or why not

7.[20 Points] What does the analysis of residuals plot reveal for the model in Question 5?

Data Set Below

Weather Baketime[minutes] BakeTemp[Degrees F] QScore

0 33 340 3.89

0 37 340 6.36

0 33 360 7.65

0 37 360 6.79

0 35 350 8.36

0 35 350 7.63

0 35 350 8.12

1 37 350 8.4

1 32 350 5.38

1 35 364 7

1 35 335 4.51

1 35 350 7.81

1 35 350 8.44

1 35 350 8.06