To draw the least-squares regression line, we first need to calculate the slope and y-intercept of the line based on the given model equation:
predicted highway mpg = 7.95 + 1.046 city mpg
The slope of the line is the coefficient of the city mpg variable, which is 1.046. The y-intercept is the constant term, which is 7.95.
Using these values, we can plot the line on a scatterplot of the data. Here is a table of the data:
Model City MPG Highway MPG
Acura RLX 20 29
BMW 530 24 34
Buick LaCrosse 20 29
Chevrolet Malibu 36 29
Ford Hybrid FWD 43 41
Honda Civic 32 42
Infiniti Q50 Red Sport 20 26
Kia Forte 30 40
Lexus ES 350 22 33
Mercedes Benz AMG S 21 30 30
Mini Cooper Clubman 24 32
Nissan Maxima 20 30
Suburu Legacy AWD 25 34
Toyota Prius ECO 53 58
To plot the line, we can start by choosing two points on the line. We can choose the points where the line intersects the minimum and maximum x-values in the data. The minimum city mpg in the data is 20, so one point on the line is (20, 7.95 + 1.046 * 20) = (20, 29.35). The maximum city mpg in the data is 43, so the other point on the line is (43, 7.95 + 1.046 * 43) = (43, 54.37).
We can now draw a straight line passing through these two points to represent the least-squares regression line.
To use the "up-and-across" method to find the predicted highway mileage of a midsized car that gets 18 mpg in the city, we can start by plotting a point at (18, 0) on the scatterplot. We can then draw a vertical line from this point to the regression line, and then draw a horizontal line from the regression line to the y-axis. The point where the horizontal line intersects the y-axis is the predicted highway mileage for a car that gets 18 mpg in the city.
Using the hand-drawn scatterplot above, we can estimate that the predicted highway mileage for a car that gets 18 mpg in the city is approximately 25.5 mpg.