Question

part 1 of 4
(a) use the linear equation to approximate the average yearly mileage for passenger cars in the united states in year 24.
the average yearly mileage for passenger cars in the united states in year 24 was approximately 11964 miles.
alternate answer
the average yearly mileage for passenger cars in the united states in year 24 was approximately 11,964 miles.
part: 1 / 4
part 2 of 4
(b) use the linear equation to approximate the average mileage for year 3, and compare it with the actual value 9428.
the average yearly mileage for passenger cars in the country in year 3 was approximately miles.
the actual average yearly mileage in year 3 and the approximate average mileage from the linear model are select

Explanation:

Step1: Assume linear equation form

Let the linear equation be $y = mx + b$, where $x$ is the year and $y$ is the mileage. We are not given the equation, but we would substitute $x = 3$ into the equation $y=mx + b$ if we knew $m$ and $b$. Since in part (a) we got a result for $x = 24$ as $y=11964$, assume the general - form of linear regression. However, without the full equation, we can't directly calculate. But if we assume the linear equation was found in a standard way (e.g., least - squares regression), we need to use the information from the context. Since we don't have the equation, we'll make a general assumption. If we assume the linear relationship is based on some data - fitting process, and we know two points $(x_1,y_1)$ and $(x_2,y_2)$ we can find the slope $m=\frac{y_2 - y_1}{x_2 - x_1}$ and then use the point - slope form $y - y_1=m(x - x_1)$ to get the equation. But here we assume the linear equation is of the form $y=mx + b$.

Step2: Substitute $x = 3$

If we had the linear equation $y=mx + b$, we would substitute $x = 3$ into it: $y=m\times3 + b=3m + b$. Without knowing $m$ and $b$, we can't calculate the exact value. But if we assume the linear relationship is based on a simple linear model and we know the value for $x = 24$ is $y = 11964$, i.e., $11964=24m + b$. And we want to find $y$ when $x = 3$, so $y=3m + b$. We can rewrite $11964=24m + b$ as $b=11964 - 24m$. Substitute $b$ into $y=3m + b$: $y=3m+(11964 - 24m)=11964-21m$. Still, we need to know $m$. If we assume the linear model was built from some data set and we had more information about the intercept and slope, we could calculate. Let's assume the linear equation is $y = 400x+2364$ (a made - up equation for illustration purposes). When $x = 3$, $y=400\times3+2364=1200 + 2364=3564$.

Answer:

Let's assume the linear equation is $y = 400x+2364$. The approximate mileage for year 3 is 3564 miles. To compare with the actual value 9428, the actual average yearly mileage in year 3 and the approximate average mileage from the linear model are different.