Question

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

Answer 1

To predict the mean daily natural gas usage for a month with an average temperature of 30°F using the regression line equation y^=1425−19.87x, substitute 30 for x, resulting in a predicted usage of 828.9 cubic feet per day.

Step-by-step explanation:

Joan's concern about energy use can be addressed by using the given regression line equation to predict her natural gas usage. The regression line provided, ŷ=1425−19.87x, represents the relationship between the mean temperature (x) and the mean amount of natural gas used per day (y).

To predict the mean amount of natural gas Joan will use per day in a month with a mean temperature of 30°F, we simply substitute x=30 into the equation:

ŷ = 1425 − 19.87(30)

Now, we perform the multiplication and subtraction:

ŷ = 1425 − 596.1

ŷ = 828.9 cubic feet

Therefore, we predict Joan will use an average of 828.9 cubic feet of natural gas per day in a month with a mean temperature of 30°F.

Answer 2

To predict Joan's daily natural gas usage at 30°F, substitute 30 for x in the regression equation, giving a predicted usage of 828.90 cubic feet per day.

Step-by-step explanation:

To predict the mean amount of natural gas Joan will use per day in a month with a mean temperature of 30°F, we simply need to plug the temperature value into the given regression equation y^ = 1425 - 19.87x.

Plugging in x = 30, we get:

y^ = 1425 - 19.87(30)

y^ = 1425 - 596.10

y^ = 828.90 cubic feet per day

So, the predicted mean amount of natural gas used per day would be 828.90 cubic feet.