Question

A study gathers data on the outside temperature during the winter, in degrees Fahrenheit, and the amount of natural gas a household consumes, in cubic feet per day. Call the temperature x and gas consumption y. The house is heated with gas, so x helps explain y. The least-squares regression line is yhat = 1344 – 19x. 1. On a day when the temperature is 20F, the regression line predicts that gas used will be about

Answer 1

The regression line predicts that the gas used will be about 964 cubic feet per day when the temperature is 20F.

Step-by-step explanation:

The regression line, yhat = 1344 - 19x, predicts the amount of natural gas consumed (y) based on the outside temperature (x). To find the predicted gas consumption when the temperature is 20F, substitute x = 20 into the regression equation:

yhat = 1344 - 19(20)

yhat = 1344 - 380

yhat = 964 cubic feet per day

Therefore, when the temperature is 20F, the regression line predicts that the gas used will be about 964 cubic feet per day.

Answer 2

The answer is "964 cubic-feet".

Step-by-step explanation:

Given regression equation:

`\to Y = 1344 - 19X\\\\\to X= 20 \ F`

Putting the value of x into the above equation:

`\to Y = 1344-19*20\\\\`

`= 1344-380\\\\= 964 \ cubic-feet`