Question

joan is concerned about the amount of energy she uses to heat her home. the scatterplot below 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 \\(\hat{y} = 1425 - 19.87 \cdot x\\).

scatterplot with x-axis: temperature (°f) from 30 to 60, y-axis: gas consumed (cubic ft) from 200 to 900, and a regression line

predict the mean amount of natural gas joan will use per day in a month with a mean temperature of 30 °f.
\\(\bigcirc\\) 70.21 cubic feet
\\(\bigcirc\\) 828.9 cubic feet
\\(\bigcirc\\) 42,730.13 cubic feet.
\\(\bigcirc\\) 73.23 cubic feet
\\(\bigcirc\\) 2021.1 cubic feet

incorrect answer

Explanation:

Step1: Identify the regression equation

The regression line is given by $\hat{y} = 1425 - 19.87 \cdot x$, where $x$ is the mean temperature and $\hat{y}$ is the predicted mean amount of natural gas used per day.

Step2: Substitute $x = 30$ into the equation

We need to find $\hat{y}$ when $x = 30$. Substitute $x = 30$ into the equation:
$$\hat{y} = 1425 - 19.87 \cdot 30$$

Step3: Calculate the value

First, calculate $19.87 \cdot 30 = 596.1$. Then, subtract this from 1425:
$$\hat{y} = 1425 - 596.1 = 828.9$$

Answer:

828.9 cubic feet