Question

Consider the 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. Use one decimal

Answer 1

Here from above T is dependent variable and L is independent variable

So the regression line is

T= L*a+b

Hence our line is

T= -7.38744*L+67.09692

1. Slope of line is -7.38744

2. r = -0.3187

Hence the R^2 = 0.1015

3.predict the value of T when L= 5

Hence we have regression equation is

T= 7.38744*L+67.09692

T=7.38744*5+67.09692

T = 30.1597

Hence the predicted T is 30.1597