Answered: The software used to compute the…

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter3: Straight Lines And Linear Functions

Section3.4: Linear Regression

Problem 12SBE: Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4

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Question

An owner of a home in the Midwest installed solar panels to reduce heating costs. After installing the solar panels, he measured the amount of natural gas used y (in cubic feet) to heat the home and outside temperature x (in degree-days, where a day's degree-days are the number of degrees its average temperature falls below 65° F) over a 23-month period. He then computed the least-squares regression line for predicting y from x and found it to be

ŷ = 85 + 16x.

The software used to compute the least-squares regression line for the equation above says that r² = 0.98.

This suggests which of the following?

1. Gas used increases by square root of 0.98 = 0.99 cubic feet for each additional degree-day?

2. Although degree-days and gas used are correlated, degree-days do not predict gas used very accurately.

3. Prediction of gas used from degree-days will be quite accurate.

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