91影视

It is given in the question that, the equation of the least-squares line is $\hat{y}=1425鈭�19.87x$

we have to identify the slope of the line and explain what it means in this setting.

When we compare our equation to the general regression equation, we get the following slope:

$b\mathit{=}\mathit{-}\mathit{19}\mathit{.}\mathit{87}$

This means that for each degree of temperature increase, the amount of gas utilized is expected to decrease by $-19.87$cubic feet.

So, the slope is :localid="1649400045461" $b=-19.87$

It is given in the question that, the equation of the least-squares line is $\hat{y}=1425鈭�19.87x$

We have to identify the y-intercept of the line. Explain why it鈥檚 risky to use this value as a prediction

When we compare our equation to the general regression equation, we get the following $y-$intercept:$a=1425$

The $y-$intercept of a regression line $\stackrel{鈭�}{y}=a+bX$is the predicted response $\stackrel{鈭�}{y}$when the explanatory variable $X=0$.

Unless $X$ is near $0$, this forecast is not statistically useful, so using this value as a prediction is risky.

We have to use the regression line to predict the amount of natural gas Joan will use in a month with an average temperature of $30$掳贵.

The line of regression is:
$\hat{y}=1425鈭�19.87x$

The regression equation becomes as follows:

Temperature islocalid="1649927707870" role="math" $\left(X\right)=30掳F$

So, the equation becomes$\stackrel{鈭�}{y}=1425-19.87\left(30\right)=828.9$