Leonard is studying the relationship between the fuel efficiency in miles per gallon (mpg), y, and the speed in miles per hour (
mph), x, of his car. He collected data for 8 different speeds and found a linear model that best fit his data: y = 18.46 + 0.16x. To analyze the fit, he found the residuals and created the following residual plot.
Using the residual plot, what conclusion can he make about the linear model he found?
A. There is a negative linear relationship between the speed and fuel efficiency.
B. There is a positive linear relationship between the speed and fuel efficiency.
C. There is a quadratic relationship between the speed and fuel efficiency.
D. There is a nonlinear relationship between the speed and fuel efficiency.
Using the residual plot, what conclusion can he make about the linear model he found?
A. There is a negative linear relationship between the speed and fuel efficiency.
B. There is a positive linear relationship between the speed and fuel efficiency.
C. There is a quadratic relationship between the speed and fuel efficiency.
D. There is a nonlinear relationship between the speed and fuel efficiency.
1 answer:
Answer:
D. There is a nonlinear relationship between the speed and fuel efficiency.
Step-by-step explanation:
A desirable residual plot should show a horizontal band with points randomly distributed about the horizontal axis.
Leonard's plot is definitely nonlinear.
The residuals show a good fit to a parabola.
This suggests that the relation between speed and fuel efficiency may be parabolic.
You might be interested in
Answer:
Tap A will take 2 hours and tap B will take 6 hours to fill the tank when turned on alone.
Step-by-step explanation:
Let tap B fills the pool alone in the time = x hours
So in one hour part of pool will be filled =
Another tap A when turned on, it takes time to fill the pool = x-5 hours
So in one hour part of the same pool filled =
Now both the taps A and B are turned on then time taken to fill the pool = 3 hours.
Part of the pool filled in one hour by both the taps =
Now we form an equation
Part of pool filled in one hour by tap A + Part of pool filled in one hour by tap B = Part of pool filled in one hour by both the taps when turned on
3(x - 4) = x(x - 5)
x² -5x = 3x - 12
x² - 8x + 12 = 0
x² - 6x - 2x + 12 = 0
x(x - 6) - 2(x - 6) = 0
(x -2)(x - 6) = 0
x = 2, 6 hours
We will take higher value of x as x = 6 hours for tap B.
Time taken by tap A = 6 - 4 = 2 hours.
Therefore, Tap A will take 2 hours and tap B will take 6 hours to fill the tank when turned on alone.