Question

Please Use Minitab

The provided data is taken from an experiment aimed at applying the two factors of temperature and alloy type as predictors of battery life.

RandOrder	Alloy	Temperature	Life
9	A1	5	140
6	A1	5	84
1	A1	5	165
4	A1	5	180
7	A1	70	34
10	A1	70	80
2	A1	70	40
5	A1	70	75
3	A1	135	15
12	A1	135	72
8	A1	135	65
11	A1	135	53
19	A2	5	160
15	A2	5	169
17	A2	5	198
20	A2	5	136
21	A2	70	136
16	A2	70	106
24	A2	70	122
18	A2	70	115
22	A2	135	20
14	A2	135	53
13	A2	135	65
23	A2	135	40
27	A3	5	143
26	A3	5	173
34	A3	5	115
32	A3	5	160
33	A3	70	174
29	A3	70	150
28	A3	70	120
25	A3	70	139
36	A3	135	91
30	A3	135	77
35	A3	135	99
31	A3	135	55

1. Develop a multiple linear regression model based on the data. Comment on the significance of linear regression (α = 0.05) and the adequacy of the model for explaining variation in the response variable.

2. Plot and analyze the residuals from the experiment. Comment on flaws in the model if any, regarding the assumptions of linear regression.

Answer 1

1)

Regression Analysis: Life versus Temperature, Alloy

Method

Categorical predictor coding (1, 0)

Analysis of Variance

Source         DF Adj SS   Adj MS F-Value P-Value
Regression      3   62483 20827.8    24.36    0.000
Temperature   1   52080 52080.2    60.91    0.000
Alloy         2   10403   5201.6     6.08    0.006
Error          32   27361    855.0
Lack-of-Fit   5   10328   2065.6     3.27    0.019
Pure Error   27   17033    630.9
Total          35   89845

Model Summary

      S    R-sq R-sq(adj) R-sq(pred)
29.2411 69.55%     66.69%      61.34%

Coefficients

Term            Coef SE Coef T-Value P-Value   VIF
Constant       133.8     10.6    12.61    0.000
Temperature -0.7167   0.0918    -7.80    0.000 1.00
Alloy
A2            26.4     11.9     2.21    0.034 1.33
A3            41.1     11.9     3.44    0.002 1.33

Regression Equation

Alloy
A1     Life = 133.8 - 0.7167 Temperature

A2     Life = 160.2 - 0.7167 Temperature

A3     Life = 174.8 - 0.7167 Temperature

Fits and Diagnostics for Unusual Observations

Obs    Life     Fit   Resid Std Resid
27 115.00 171.25 -56.25      -2.06 R

R Large residual