The swinging pendulum Refer to Exercise 31. We took the logarithm (base 10) of the values for both variables. Some computer output from a linear regression analysis on the transformed data is shown below.

Regression Analysis: log(Period) versus log(Length)

Predictor Coef SE Coef T P Constant -0.73675 0.03808 -19.35 0.000 log(Length) 0.51701 0.02511 20.59 0.000 S = 0.0185568 R-Sq = 97.9% R-Sq(adj) = 97.7%

(a) Based on the output, explain why it would be reasonable to use a power model to describe the relationship between the length and period of a pendulum.

(b) Give the equation of the least-squares regression line.

Be sure to define any variables you use.

Transcribed Image Text:

Residual log(Period) 03- 0.2- 01- 0.0 -01- 12 13 14 15 16 17 18 1.9 2.0 2.1 log(Length) 0.03- 0.02- 0.01 0.00- -0.01- -0.02- -0.03- 1.2 1.3 1.4 1.5 16 17 18 19 2.0 2.1 log(Length)