Question

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.

I need to find the QS for time and temp to be able to fit the equation ?

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

Answer 1

Let Y=QScore , X1=Baketime , X2=Temp

The complete second order model which uses intraction of time and temp is given as

Now using Minitab we can fit the regression easily as follows:

1: Insert the columns = Y,X1 ,X2, X1^2, X2^2, X1X2

2: then go to STAT=>Regression=>Regression

3: Insert Y as response variable and X1,X2,X1^2,X2^2,X1*X2 as predictor variables and hit ok!

following is the output of Minitab

The regression equation is
y = - 2142 + 28.4 x1 + 9.33 x2 - 0.193 X1^2 - 0.0111 X2^2 - 0.0416 X1*X2

Predictor Coef SE Coef T P
Constant -2142.4 199.4 -10.74 0.000
x1 28.379 4.154 6.83 0.000
x2 9.3327 0.9554 9.77 0.000
X1^2 -0.19318 0.03826 -5.05 0.001
X2^2 -0.011124 0.001288 -8.64 0.000
X1*X2 -0.041625 0.009123 -4.56 0.002

S = 0.364933 R-Sq = 96.3% R-Sq(adj) = 94.0%

Analysis of Variance

Source DF SS MS F P
Regression 5 27.6102 5.5220 41.46 0.000
Residual Error 8 1.0654 0.1332
Total 13 28.6756

Source DF Seq SS
x1 1 4.1135
x2 1 7.6613
X1^2 1 3.1236
X2^2 1 9.9396
X1*X2 1 2.7722

Have an awesom day...