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Joan is concerned about the amount of energy she uses to heat her home.

The scatterplot shows the relationship between x = mean temperature in a particular month

and y = mean amount of natural gas used per day (in cubic feet) in that month, along with the regression line y^=1425−19.87x

a. Predict the mean amount of natural gas Joan will use per day in a month with a mean temperature of 30°F.

b. Predict the mean amount of natural gas Joan will use per day in a month with a mean temperature of 65°F.

c. How confident are you in each of these predictions? Explain your reasoning.

Short Answer

Expert verified

Part (a) Joan will use an average of 828.90cubic feet of natural gas per day in a month with a mean temperature of 30degrees Fahrenheit.

Part (b) Joan will need 133.45cubic feet of natural gas each day in a month with a mean temperature of 65degrees Fahrenheit.

Part (c) As per the given parts (a) and (b) there is no surety that the prediction is correct.

Step by step solution

01

Part (a) Step 1: Given information

x:The average temperature for a given month.

y:In that month, the average amount of natural gas utilized each day.

The following is the OLS regression line:

yÁåœ=1425−19.87x

02

Part (a) Step 2: Concept

The most common method for fitting a line to a scatterplot is least squares.

03

Part (a) Step 3: Calculation

With a mean temperature of 30°F, the estimated average amount of natural gas Joan will need every day in a month can be computed as follows:

yÁåœ=1425−19.87(30)

=828.90

04

Part (b) Step 1: Calculation

A mean temperature of30°F the amount of natural gas Joan will need every day in a month may be computed as:

yÁåœ=1425−19.87(65)

=133.45

05

Part (c) Step 1: Explanation

Using a regression line to make a forecast is just a mathematical calculation that may or may not be accurate. As a result, the value projected above may or may not be right or true. As a result, there is no guarantee that the prognosis is accurate.

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