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Automobile fuel efficiency is often measured in miles per gallon (mpg) that the car can be driven per gallon of fuel (highway mpg). Suppose we have a collection of cars. We measure their weights and fuel efficiencies, and generate the following scatterplot:

**Scatterplot: Highway MPG vs Weight**

Which equation is a reasonable description of the least-squares regression line for the predicted highway mpg?

A. predicted highway mpg = 52.3 – 0.0067 (weight)
B. predicted highway mpg = 52.3 + 0.0067 (weight)
C. predicted highway mpg = 32.3 – 0.0067 (weight)
D. predicted highway mpg = 32.3 + 0.0067 (weight)
E. predicted highway mpg = 36.3 – 12.3 (weight)
F. predicted highway mpg = 36.3 + 12.3 (weight)

Answer :

To determine the reasonable equation for the least-squares regression line for the predicted highway MPG based on weight, we need to consider the scatterplot. In a scatterplot, the least-squares regression line represents the best-fit line that minimizes the distance between the observed data points and the line.

Looking at the given equation options, we can eliminate those with a positive coefficient for weight (since weight is typically expected to negatively impact fuel efficiency) and those with a constant term significantly different from the observed data points.

Out of the remaining options, the equation "predicted highway mpg = 32.3 – 0.0067 (weight)" seems the most reasonable. This equation suggests that as the weight of the car increases, the predicted highway MPG decreases.

The equation of a regression line is typically written as y = mx + b, where y represents the dependent variable, x represents the independent variable, m represents the slope of the line, and b represents the y-intercept.

The slope, m, represents the rate of change of y with respect to x, while the y-intercept, b, represents the predicted value of y when x is zero.

The constant term (32.3) aligns reasonably with the observed data points, and the negative coefficient for weight reflects the expected negative relationship between weight and fuel efficiency.

Therefore, the equation "predicted highway mpg = 32.3 – 0.0067 (weight)" is a reasonable description of the least-squares regression line for the predicted highway MPG based on weight.

To know more about regression, refer here :

https://brainly.com/question/32505018#

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