The Quality of a product depends on temperature and Pressure (in PSI). Use the 2
ID: 2985678 • Letter: T
Question
The Quality of a product depends on temperature and Pressure (in PSI). Use the 27 observations in the table and answer the following questions:
Quality
Temp
PSI
Quality
Temp
PSI
50.80
80
50
97.40
90
55
50.70
80
50
70.90
90
60
49.40
80
50
68.80
90
60
93.70
80
55
71.30
90
60
90.90
80
55
46.60
100
50
90.90
80
55
49.10
100
50
74.50
80
60
46.60
100
50
73.00
80
60
69.80
100
55
71.20
80
60
72.50
100
55
63.40
90
50
73.20
100
55
61.60
90
50
38.70
100
60
63.40
90
50
42.50
100
60
93.80
90
55
41.40
100
60
92.10
90
55
1. Fit a first-order model to the data (make sure you include both independent variables.)
2. Report the equation of the model.
3. Interpret the estimated regression coefficients.
4. Report the coefficient of determination and the standard error of estimate for the first-order model. Based on these, how good is the model?
5. Fit an interaction model to the data.
6. Report the coefficient of determination and the standard error of estimate for the interaction model. Based on these, how good is the model?
7. Fit a complete second-order model to the data.
8. Report the coefficient of determination and the standard error of estimate for the complete second-order model. Based on these, how good is the model?
9. Which of the three models do you prefer? Why? Explain.
Quality
Temp
PSI
Quality
Temp
PSI
50.80
80
50
97.40
90
55
50.70
80
50
70.90
90
60
49.40
80
50
68.80
90
60
93.70
80
55
71.30
90
60
90.90
80
55
46.60
100
50
90.90
80
55
49.10
100
50
74.50
80
60
46.60
100
50
73.00
80
60
69.80
100
55
71.20
80
60
72.50
100
55
63.40
90
50
73.20
100
55
61.60
90
50
38.70
100
60
63.40
90
50
42.50
100
60
93.80
90
55
41.40
100
60
92.10
90
55
Explanation / Answer
A) do the regression taking quality as dependent variable and temp and psi as independent variable.In which taking both temp and psi as linear variable
B) quality = 106.11 -.9.1 temp + 0.78psi
C) regression coefficients are 106.11 , -9.1 and 0.78
D) coefficient of determination = 0.145 and standard error = 16.66
as coefficient of determination is low so linear eq is not fitting in model correctly
E) Quality = -615.76 + 7.1 temp +13.91 psi -0.145 ( temp* psi)
F) coefficient of determination = 0.193 and standard error = 16.19
as coefficient of determination is low so linear eq is not fitting in model correctly but it is better than linear model
7) quality = -4405.41 + 23.07 temp + 126.60psi - 0.133 temp^2 - 1.14 psi^2
8)coefficient of determination = 0.90 and standard error = 5.62
as coefficient of determination is high so linear eq is fitting in model correctly and it is better than above the two model
9) second order model the best model as the coefficient of determination is highest in this model and standard error is lowest which makes the model best fit in the equation
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