Answer :
In this problem, we have the following equation:
[tex]\hat{y}=P(x)=38,257-0.1629\cdot x.[/tex]$\hat{y}=P(x)=38,257-0.1629\cdot x.$Where:
• y^ = P(x) = Price of x miles driven by a Ford F-150's,
,• x = # of miles driven by a Ford F-150's.
a) For x = 100,000, we get:
[tex]P(100,000)=21,967.[/tex]b) The general equation of a line is:
[tex]y=b+m\cdot x\text{.}[/tex]Where:
• b = y-intercept,
,• m = slope.
Comparing the general equation with the equation of the problem, we have:
[tex]m=-0.1629.[/tex]Because the dependent and the independent variables are:
• y = Price of x miles driven by a Ford F-150's,
,• x = # of miles driven by a Ford F-150's.
The slope m with its units is:
[tex]m=-0.1629\cdot\frac{\text{units of price}}{\text{miles driven}}\text{.}[/tex]c) Comparing the equation of the problem and the general equation of a line, we find the value of the y-intercept:
[tex]b=38,257.[/tex]The value of the y-intercept is the value of y when we have x = 0, i.e. when we have driven 0 miles. The units of the y-intercept are the same as the variable y, so the y-intercept with units is:
[tex]b=38,257\text{ units of price.}[/tex]d) Replacing the value x = 58,000 in the equation of the line, we get:
[tex]\hat{y}=38,257-0.1629\cdot58,000=28,808.8.[/tex]The residual is the difference between the y coordinate of the point (58,000, $30,000) and the value of y^ that we have computed:
[tex]\text{Residual = }y-\hat{y}=30,000-28,808.8=1,191.2[/tex]Answers
a) The price for 100,000 driven is $21,967.
b) The slope of the line is the price per unit of a mile driven:
[tex]m=-0.1629\cdot\frac{\text{units of price}}{\text{miles driven}}\text{.}[/tex]c) The y-intercept of the line is the cost of when the number of miles driven is zero:
[tex]b=38,257\text{ units of price.}[/tex]d) Residual = $1,191.2.