An engineer wants to determine how the weight of a car, x, affects gas mileage,
ID: 3203576 • Letter: A
Question
An engineer wants to determine how the weight of a car, x, affects gas mileage, y. The following data represent the weights of various cars and their miles per gallon. Car Weight (pounds), x 2720 2955 3275 3795 4120 22.9 24.2 22.5 18.9 15.4 Miles per Gallon, y (a) Find the least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable Write the equation for the least-squares regression line y- x (Round to four decimal places as needed.) (b) Interpret the slope and intercept, if appropriate. Choose the best interpretation for the slope. O A. The slope indicates the mean change in miles per gallon for an increase of 1 pound in weight. O B. T slope indicates the mean miles per gallon he O C. The slope indicates the mean weight. o D. The slope indicates th ratio between the mean weight and the mean miles per gallon O E. It is not appropriate to interpret the slope because it is not equal to zeroExplanation / Answer
> x = c(2720,2955,3275,3795,4120)
> y = c(22.9,24.2,22.5,18.9,15.4)
> summary(lm(y~x))
Call:
lm(formula = y ~ x)
Residuals:
1 2 3 4 5
-1.6592 1.0008 1.1528 0.5623 -1.0568
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 40.301041 4.334032 9.299 0.00263 **
x -0.005787 0.001270 -4.557 0.01981 *
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 1.474 on 3 degrees of freedom
Multiple R-squared: 0.8738, Adjusted R-squared: 0.8317
F-statistic: 20.77 on 1 and 3 DF, p-value: 0.01981
(a)
Equation is
y = -0.0058x + 40.3010
(b)
A. The slope indicates the mean change in miles per gallon on increase of 1 pound in weight.
Here it is a decrease of 0.0058 miles per gallon
y-intercept
Option E
It is not appropriate since weight of 0 gallon is unrealistic.
(c)
Predicted value =
-0.0058*3275 + 40.3010
= 21.31
The predicted value is below the observed value.
Hence the value is above average.
22.5-21.31 =1.19
Graph D is the best respresentation of the regression line along with the residual.