Question
In: Statistics and Probability
Consider the following data of experimental data measuring the lifetime of a wire as a function...
Consider the following data of experimental data measuring the lifetime of a wire as a function of temperature
|
Temp |
200 |
200 |
200 |
200 |
200 |
200 |
|
Lifetime |
5933 |
5404 |
4947 |
4963 |
3358 |
3878 |
|
Temp |
220 |
220 |
220 |
220 |
220 |
220 |
|
Lifetime |
1561 |
1494 |
747 |
768 |
609 |
777 |
|
Temp |
240 |
240 |
240 |
240 |
240 |
240 |
|
Lifetime |
258 |
299 |
209 |
144 |
180 |
184 |
- Sketch scatter plots of untransformed data and of ln(lifetime) vs 1/temp
- Estimate the lifetime of the wire at t=230 using the better model, be it untransformed or transformed.
Solutions
Expert Solution
| Temp (x) | Lifetime (y) | ln(y) | 1/x |
| 200 | 5933 | 8.6883 | 0.0050 |
| 200 | 5404 | 8.5949 | 0.0050 |
| 200 | 4947 | 8.5065 | 0.0050 |
| 200 | 4963 | 8.5098 | 0.0050 |
| 200 | 3358 | 8.1191 | 0.0050 |
| 200 | 3878 | 8.2631 | 0.0050 |
| 220 | 1561 | 7.3531 | 0.0045 |
| 220 | 1494 | 7.3092 | 0.0045 |
| 220 | 747 | 6.6161 | 0.0045 |
| 220 | 768 | 6.6438 | 0.0045 |
| 220 | 609 | 6.4118 | 0.0045 |
| 220 | 777 | 6.6554 | 0.0045 |
| 240 | 258 | 5.5530 | 0.0042 |
| 240 | 299 | 5.7004 | 0.0042 |
| 240 | 209 | 5.3423 | 0.0042 |
| 240 | 144 | 4.9698 | 0.0042 |
| 240 | 180 | 5.1930 | 0.0042 |
| 240 | 184 | 5.2149 | 0.0042 |
a) Untransformed
Using Excel, insert scatter plot with temp on x-axis and lifetime on y-axis.
Right click on any point, select Add Trendline, choose Linear and tick Display Equation on Chart and Display R-square value on Chart
Transformed
Using Excel, insert scatter plot with 1/temp on x-axis and ln(lifetime) on y-axis.
Right click on any point, select Add Trendline, choose Linear and tick Display Equation on Chart and Display R-square value on Chart
b) Since R2 of transformed model is more (0.9543) than untranssformed model (0.8113), transformed model is better.
At lifetime = 230,
y = 3735.5x - 10.205
ln(lifetime) = 3735.5*(1/230) - 10.205
= 6.036
lifetime = exp(6.036) = 418.344
orchestra answered 2 years agoRelated Solutions
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