Question
In: Statistics and Probability
The weight of a car can influence the mileage that the car can obtain. A random...
The weight of a car can influence the mileage that the car can obtain. A random sample of 20 cars was taken and the weight (in pounds) and mileage (in mpg) were recorded and are in the table below.
| X, weight | Y, mileage |
|---|---|
| 4000 | 23.1 |
| 4500 | 17.2 |
| 4500 | 19.5 |
| 2250 | 53.3 |
| 2750 | 46.9 |
| 3500 | 31.3 |
| 4500 | 17 |
| 4000 | 23.6 |
| 2750 | 36.3 |
| 3000 | 31.5 |
| 3000 | 31.4 |
| 3000 | 32.2 |
| 4000 | 23.4 |
| 2500 | 40.9 |
| 3000 | 31.4 |
| 3500 | 31.3 |
| 3500 | 32.6 |
| 3000 | 32.2 |
| 2250 | 41.1 |
| 3500 | 28 |
a) State the random variables.
rv X =
of rv Y = of
b) The symbol and value of the correlation coefficient are as follows:
Round final answer to 3 decimal places.
=
Interpret this value:
- There is a strong
- relation between weight and mileage for cars.
c) The symbol and value of the coefficient of determination are as follows:
Round final answer to 3 decimal places.
=
Interpret this value:
- About % of the
explained by the linear model with as its variable.
Solutions
orchestra answered 2 years agoRelated Solutions
The weight of a car can influence the mileage that the car can obtain. A random...
The weight of a car can influence the mileage that the car can
obtain. A random sample of 20 cars’ weights and mileage is
collected. The table for the weight and mileage of the cars is
given below. Use Excel to find the best fit linear regression
equation, where weight is the explanatory variable. Round the slope
and intercept to three decimal places.
Weight Mileage
30.0 32.2
20.0 56.0
20.0 46.2
45.0 19.5
40.0 23.6
45.0 16.7
25.0 42.2
55.0 ...
CAR 1 MILEAGE CAR 2 MILEAGE CAR 3 MILEAGE CAR 4 MILEAGE 1 14.9 2 10.8...
CAR 1
MILEAGE
CAR 2
MILEAGE
CAR 3
MILEAGE
CAR 4
MILEAGE
1
14.9
2
10.8
3
19
4
18.9
1
17.7
2
10.7
3
13.8
4
19.2
1
17.7
2
11
3
20.1
4
19.4
1
18.7
2
12
3
19.8
4
21
1
19.8
2
7.5
3
12.2
4
13.5
1
21.1
2
10.5
3
24.3
4
17.2
1
17.3
2
9.1
3
21.8
4
12.7
1
19.8
2
10.7
3
20.7
1
16.3
2
7.5
3
16.4...
CAR 1 MILEAGE CAR 2 MILEAGE CAR 3 MILEAGE CAR 4 MILEAGE 1 14.9 2 10.8...
CAR 1
MILEAGE
CAR 2
MILEAGE
CAR 3
MILEAGE
CAR 4
MILEAGE
1
14.9
2
10.8
3
19
4
18.9
1
17.7
2
10.7
3
13.8
4
19.2
1
17.7
2
11
3
20.1
4
19.4
1
18.7
2
12
3
19.8
4
21
1
19.8
2
7.5
3
12.2
4
13.5
1
21.1
2
10.5
3
24.3
4
17.2
1
17.3
2
9.1
3
21.8
4
12.7
1
19.8
2
10.7
3
20.7
1
16.3
2
7.5
3
16.4...
CAR 1 MILEAGE CAR 2 MILEAGE CAR 3 MILEAGE CAR 4 MILEAGE 1 14.9 2 10.8...
CAR 1
MILEAGE
CAR 2
MILEAGE
CAR 3
MILEAGE
CAR 4
MILEAGE
1
14.9
2
10.8
3
19
4
18.9
1
17.7
2
10.7
3
13.8
4
19.2
1
17.7
2
11
3
20.1
4
19.4
1
18.7
2
12
3
19.8
4
21
1
19.8
2
7.5
3
12.2
4
13.5
1
21.1
2
10.5
3
24.3
4
17.2
1
17.3
2
9.1
3
21.8
4
12.7
1
19.8
2
10.7
3
20.7
1
16.3
2
7.5
3
16.4...
1, An engineer wanted to determine how the weight of a car affects gas mileage. The...
1, An engineer wanted to determine how the weight of a car
affects gas mileage. The accompanying data represent the weights of
various domestic cars and their gas mileage in the city for a
certain model year. Suppose that we add Car 12 to the original
data. Car 12 weighs 3,305 pounds and gets 19 miles per gallon.
Complete parts(a) through (f) below.
Car
Weight (lbs)
Miles per Gallon
1
3765
19
2
3984
18
3
3590
21
4
3175...
The table shows a short excerpt from the "car weight and mileage" data file on the...
The table shows a short excerpt from the "car weight and
mileage" data file on the text CD. That file lists several 2004
model cars with automatic transmission and their x =
weight (in pounds) and y = mileage (miles per gallon of
gas). The scatterplot is roughly linear and r = -0.74. The
regression equation is = 47.140 - 0.0051x.
Automobile Brand
Weight
Mileage
Honda Accord Sedan LX
3137
35
Toyota Corolla
2583
40
Dodge Dakota Club Cab
3869
20...
An engineer wants to determine how the weight of a? car, x, affects gas? mileage, y....
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
A
B
C
D
E
Weight? (pounds), x
25452545
31003100
34103410
37703770
40404040
Miles per? Gallon, y
25.225.2
23.923.9
19.619.6
18.518.5
14.314.3
?(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...
An engineer wants to determine how the weight of a car, x, affects gas mileage, y....
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 Miles per Gallon,
y
A 2695 26.7
B 2975 23.6
C 3260 24.9
D 3760 23.1
E 4225 20.4
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...
An engineer wants to determine how the weight of a gas-powered car, x, affects gas mileage,...
An engineer wants to determine how the weight of a gas-powered
car, x, affects gas mileage, y. The accompanying data represent
the weights of various domestic cars and their miles per gallon in
the city for the most recent model year. Complete parts (a)
through (d) below.
Weight (pounds), x Miles per Gallon, y
3736 17
3938 17
2746 24
3485 19
3250 22
3035 24
3826 16
2506 23
3387 18
3847 18
3251 17
(a) Find the least-squares...
An engineer wants to determine how the weight of a gas-powered car, x, affects gas mileage,...
An engineer wants to
determine how the weight of a gas-powered car, x, affects gas
mileage, y. The accompanying data represent the weights of various
domestic cars and their miles per gallon in the city for the most
recent model year. Complete parts (a) through (d) below.
Click here to
view the weight and gas mileage data.
Weight
(pounds),
x
Miles
per
Gallon,
y
3711
16
3828
17
2625
24
3648
19
3313
21
2914
24
3786
17
2694
23...
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