Homework SourseDetermine the regression equation to predict Temperature bas
Determine the regression equation to predict Temperature based upon the following experimental data:
Stress (N/m2)
Weight (kg)
Voltage (mV)
Current (mA)
Temperature
8
39
54
36
5680
8
39
52
34
5612
9
41
50
32
5598
9
42
48
30
5570
10
42
47
28
5550
12
44
47
26
5508
14
44
46
25
5488
16
45
45
22
5425
17
46
44
20
5400
17
48
43
20
5395
19
51
41
18
5322
20
53
40
18
5200
22
54
38
15
5180
24
56
36
12
5144
26
66
35
10
5111
28
77
34
8
5056
Be sure to explain how/why you developed your regression equation and support your decisions using appropriate Minitab outputs. Include the appropriate Minitab outputs.
| Stress (N/m2) | Weight (kg) | Voltage (mV) | Current (mA) | Temperature |
| 8 | 39 | 54 | 36 | 5680 |
| 8 | 39 | 52 | 34 | 5612 |
| 9 | 41 | 50 | 32 | 5598 |
| 9 | 42 | 48 | 30 | 5570 |
| 10 | 42 | 47 | 28 | 5550 |
| 12 | 44 | 47 | 26 | 5508 |
| 14 | 44 | 46 | 25 | 5488 |
| 16 | 45 | 45 | 22 | 5425 |
| 17 | 46 | 44 | 20 | 5400 |
| 17 | 48 | 43 | 20 | 5395 |
| 19 | 51 | 41 | 18 | 5322 |
| 20 | 53 | 40 | 18 | 5200 |
| 22 | 54 | 38 | 15 | 5180 |
| 24 | 56 | 36 | 12 | 5144 |
| 26 | 66 | 35 | 10 | 5111 |
| 28 | 77 | 34 | 8 | 5056 |
Solution
Use the excel \"data analysis\" add on for regression. You will get the following output -
In minitab, you will get the following output from the \'linear regression\'-
Regression Analysis: Temperature versus Stress (N/m2, Weight (kg), Voltage (mV), Current (mA)
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 4 588363 147091 274.26 0.000
Stress (N/m2) 1 8982 8982 16.75 0.002
Weight (kg) 1 469 469 0.87 0.370
Voltage (mV) 1 10237 10237 19.09 0.001
Current (mA) 1 4155 4155 7.75 0.018
Error 11 5900 536
Total 15 594263
Model Summary
S R-sq R-sq(adj) R-sq(pred)
23.1587 99.01% 98.65% 97.92%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 4810 283 17.02 0.000
Stress (N/m2) -28.69 7.01 -4.09 0.002 59.78
Weight (kg) 1.53 1.64 0.94 0.370 8.01
Voltage (mV) 32.25 7.38 4.37 0.001 55.37
Current (mA) -19.97 7.17 -2.78 0.018 104.97
Regression Equation
Temperature = 4810 - 28.69 Stress (N/m2) + 1.53 Weight (kg) + 32.25 Voltage (mV)
- 19.97 Current (mA)
Fits and Diagnostics for Unusual Observations
Obs Temperature Fit Resid Std Resid
12 5200.0 5247.8 -47.8 -2.36 R
R Large residual
| SUMMARY OUTPUT | ||||||||
| Regression Statistics | ||||||||
| Multiple R | 0.99502385 | |||||||
| R Square | 0.990072462 | |||||||
| Adjusted R Square | 0.986462448 | |||||||
| Standard Error | 23.15867812 | |||||||
| Observations | 16 | |||||||
| ANOVA | ||||||||
| df | SS | MS | F | Significance F | ||||
| Regression | 4 | 588363.3694 | 147090.8424 | 274.2572406 | 6.19268E-11 | |||
| Residual | 11 | 5899.568093 | 536.3243721 | |||||
| Total | 15 | 594262.9375 | ||||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
| Intercept | 4810.027615 | 282.6505758 | 17.01757586 | 2.99887E-09 | 4187.917892 | 5432.137338 | 4187.917892 | 5432.137338 |
| Stress (N/m2) | -28.68688608 | 7.009867513 | -4.092357812 | 0.001782375 | -44.11550045 | -13.2582717 | -44.11550045 | -13.2582717 |
| Weight (kg) | 1.529938229 | 1.635836224 | 0.935263694 | 0.369730264 | -2.070513024 | 5.130389483 | -2.070513024 | 5.130389483 |
| Voltage (mV) | 32.24818654 | 7.381380627 | 4.368855661 | 0.00111967 | 16.00187732 | 48.49449576 | 16.00187732 | 48.49449576 |
| Current (mA) | -19.96985962 | 7.174556765 | -2.783427642 | 0.01779449 | -35.76095259 | -4.178766648 | -35.76095259 | -4.178766648 |
