To find the line of regression, we first need to calculate the slope (b) and the y-intercept (a) using the given data points. Then, we can use the line of regression equation (y^ = a + bx) to find the best predicted new mileage rating.
Given data:
Old:
x (mi/gal): 16, 27, 17, 33, 28, 24, 18, 22, 20, 29, 21
y (mi/gal): 15, 24, 15, 29, 25, 22, 16, 20, 18, 26, 19
n = 11
Sum of x (Σx): 235
Sum of y (Σy): 219
Sum of x^2 (Σx^2): 5535
Sum of xy (Σxy): 5186
Slope (b):
b = (nΣxy - ΣxΣy) / (nΣx^2 - (Σx)^2)
b = (11*5186 - 235*219) / (11*5535 - 235^2)
b = (57046 - 51465) / (60885 - 55225)
b = 5581 / 5660
b = 0.986
Y-intercept (a):
a = (Σy - bΣx) / n
a = (219 - 0.986*235) / 11
a = (219 - 231.91) / 11
a = -12.91 / 11
a = -1.173
Therefore, the line of regression is:
y^ = -1.173 + 0.986x
Now, we can find the best predicted new mileage rating for a four-wheel-drive vehicle with an old rating of 19 mi/gal:
y^ = -1.173 + 0.986(19)
y^ = -1.173 + 18.634
y^ = 17.46 mi/gal
So, the best predicted new mileage rating for a four-wheel-drive vehicle with an old rating of 19 mi/gal is 17.46 mi/gal.
Therefore, the correct answer is:
y^ = -1.173 + 0.986x; 17.46 mi/gal
Determine the line of regression and use it to find the best predicted new mileage rating of a four-wheel-drive vehicle given that the old rating is 19 mi/gal.
Old
16
27
17
33
28
24
18
22
20
29
21
New
15
24
15
29
25
22
16
20
18
26
19
(1 point)
Responses
y^ = 0.808 + 0.863x; 18.1
mi/gal
y^ = 0.863 + 0.808x; 16.2
mi/gal
y^ = 0.863 + 0.808x; 22.4
mi/gal
y^ = 0.808 + 0.863x; 17.2
mi/gal
1 answer