Math Problem Statement

Grandfather clocks use pendulums to keep accurate time. The relationship between the length of a pendulum L and the time T for one complete oscillation can be determined from the data in the table shown. a. Find the least squares line equation and graph it simultaneously with the data​ points, with L as the horizontal axis and T as the vertical axis. Does it seem to fit the​ data? b. Find the correlation coefficient and interpret it. Does it confirm your answer to part​ (a)?

Solution

To help with parts (a) and (b), I will need the data from the table. Could you please provide the values for the pendulum length LL and the time TT for one complete oscillation? This will allow me to calculate the least squares line, graph it, and then analyze the correlation coefficient for you.

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Math Problem Analysis

Mathematical Concepts

Statistics
Linear Regression
Correlation
Graphing

Formulas

Least Squares Line equation: T = mL + b
Correlation coefficient formula: r = Σ[(xi - x̄)(yi - ȳ)] / √(Σ(xi - x̄)² * Σ(yi - ȳ)²)

Theorems

Least Squares Method
Pearson Correlation Coefficient

Suitable Grade Level

Grades 11-12