Question

In: Statistics and Probability

Second data set: L    T 0.5 1.915684 0.7 1.29032 0.9 1.90683 1.1 1.840219 1.3 2.668192...

Second data set:

L    T
0.5 1.915684
0.7 1.29032
0.9 1.90683
1.1 1.840219
1.3 2.668192
1.5 2.432488
1.7 2.91615
1.9 2.731426
2.1 2.659927
2.3 2.662569
2.5 2.847514
2.7 3.754418
2.9 3.675227
3.1 3.363444
3.3 3.377861
3.5 4.080403
3.7 4.38519
3.9 4.073612
4.1 4.356581
4.3 4.27699

For this data we do not know how T depends on L. We hope that T is proportional to some power of L. Transform data by taking Logarithms and do linear regression. Upon computing the regression round to one decimal

1.What is the slope?

2.What is R2? Use two decimals

3.Predict the value of T when L = 5.5. Use one decimal

Solutions

Expert Solution

1)

ln T^ = 0.7052 + 0.5036 ln L

slope = 0.5036

2)

R^2 = 0.8571

3)

L = 5.5

ln T^ = 0.7052 + 0.5036 ln (5.5)

= 1.5637

T^ = e^(1.5637)

= 4.7765


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