Chapter 3.2, Problem 42E

(a)

To determine

To interpret the slope of the regression line.

Explanation of Solution

It is given in the question the regression line that,

  $\widehat{y}=1425-19.87x$

Thus as we know that the slope is coefficient of x in the least square regression equation and represents the average increase or decrease of y per unit of x . Thus, the slope is,

  $b_1=-19.87$

This then implies that on average, the mean amount of natural gas Joan will use per day in a month decrease by $-19.87$ cubic feet per degree Fahrenheit.

(b)

To determine

To explain does the value of the y -intercept have meaning in this context and if so then interpret the y -intercept.

Answer to Problem 42E

It does have meaning.

Explanation of Solution

It is given in the question the regression line that,

  $\widehat{y}=1425-19.87x$

As we know that, the y -intercept is the constant in the least square regression equation and represents the average y -value when x is zero. Thus, the y -intercept is as:

  $b_0=1425$

This then implies that on average, the mean amount of natural gas used per day is $1425$ cubic feet when the temperature is zero degree Fahrenheit. Since a temperature of zero degree Fahrenheit is plausible the y -intercept has meaning in this context.