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Chapter 3: Q. 4 (page 158)

Joan is concerned about the amount of energy she uses to heat her home. The graph below plots the mean number of cubic feet of gas per day that Joan used each month against the average temperature that month (in degrees Fahrenheit) for one heating season.

(a) Does the plot show a positive or negative association between the variables? Why does this make sense?

(b) What is the form of the relationship? Is it very strong? Explain your answers.

(c) Explain what the point at the bottom right of the plot represents.

Short Answer

Expert verified

(a) The scatter plot shows a negative association between the variables, this makes logical sense because as the temperature increases there is less need to consume gas to heat the house.

(b) We have strong linear relationships.

(c) The point at the bottom right shows a high temperature, with a small amount of gas consumed.

Step by step solution

01

Part(a) Step 1: Given Information 

The graph below plots the mean number of cubic feet of gas per day.

02

Part(a) Step 2: Explanation 

As the temperature (the explanatory variable) increases, the amount of gas consumed (the response variable) will decrease as the house is naturally warmer by the temperature. Read a scatter plot from left to right, if the points are drifting in the downward direction the scatter plot shows a negative association. Another way to determine a negative correlation is if either variable increases as the other variable decreases.

03

Part(b) Step 1: Given Information 

The graph below plots the mean number of cubic feet of gas per day.

04

Part(b) Step 2: Explanation 

The points in the scatterplot seem to roughly line on a line and thus the relationship between the variable is roughly linear. Since the linear pattern is obvious from the scatterplot, the relationship is also strong.

05

Part(c) Step 1: Given Information 

The graph below plots the mean number of cubic feet of gas per day.

06

Part(c) Step 2: Explanation 

The point at the right bottom describes a month where the average temperature was about 58 degrees Fahrenheit and there are approximately 250 cubic feet of gas consumed that month.

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