Question

the table shows a countrys average fuel consumption for \light duty\ vehicles (passenger cars and small trucks) for several years. let x be the number of years since 1985, so that x = 5 stands for 1990 and so forth.
(a) find the linear regression model for these data. what does the slope in the regression model represent?
(b) use the linear regression model to predict the countrys average fuel economy for light duty vehicles in the year 2035.
(a) find the linear regression model for these data. choose the correct answer below.
y = 0.15x+16.6
(use integers or decimals for any numbers in the equation. round to the nearest hundredth as needed.)
what does the slope in the regression model represent?
(round to the nearest hundredth as needed.)
a. the slope says that the average fuel economy for light duty vehicles increases about mpg per year.
b. the slope says that the average fuel economy for light duty vehicles decreases about mpg per year.

Explanation:

Step1: Identify the linear regression model

The given linear - regression model is $y = 0.15x+15.6$, where $y$ is the fuel economy (mpg) and $x$ is the number of years since 1985.

Step2: Analyze the slope

In a linear equation of the form $y=mx + b$ (where $m$ is the slope and $b$ is the y - intercept), for the equation $y = 0.15x+15.6$, the slope $m = 0.15$. Since the slope is positive, it means that the value of $y$ (average fuel economy for light - duty vehicles) increases as $x$ (number of years since 1985) increases.

Step3: Predict for 2035

First, find $x$ for the year 2035. Since $x$ is the number of years since 1985, for 2035, $x=2035 - 1985=50$.
Substitute $x = 50$ into the equation $y=0.15x + 15.6$.
$y=0.15\times50+15.6$.
$y = 7.5+15.6$.
$y=23.1$.

Answer:

a. The linear regression model is $y = 0.15x+15.6$. The slope says that the average fuel economy for light - duty vehicles increases about $0.15$ mpg per year.
b. The predicted average fuel economy for light - duty vehicles in 2035 is $23.1$ mpg.