Refer to Exercise 33. We took the logarithm (base 10) of the values for both length and period. Here is some computer output from a linear regression analysis of the transformed data.

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.

c. Use the model from part (b) to predict the period of a pendulum with length 80 cm.

Exercise 33.

Mrs. Hanrahan’s precalculus class collected data on the length (in centimeters) of a pendulum and the time (in seconds) the pendulum took to complete one back-andforth swing (called its period). The theoretical relationship between a pendulum’s length and its period is

where g is a constant representing the acceleration due to gravity (in this case, g = 980 cm/s²). Here is a graph of period versus length, along with output from a linear regression analysis using these variables.

Transcribed Image Text:

0.3 0.2 0.1 0.0 -0.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 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 1.6 1.7 1.8 1.9 2.0 2.1 log (length) Residual log (period)