Question
In: Math
The data in the table represent the weights of various domestic cars and their miles per...
The data in the table represent the weights of various domestic cars and their miles per gallon in the city for the 2008 model year. For these data, the least-squares regression line is ModifyingAbove y with -0.006x + 42.216. A twelfth car weighs 3,425 pounds and gets 12 miles per gallon.
(a) Compute the coefficient of determination of the expanded data set. What effect does the addition of the twelfth car to the data set have on Rsquared?
(b) Is the point corresponding to the twelfth car influential? Is it an outlier?
Car, Weight (pounds) x, Miles per Gallon y
1 3766 20
2 3989 21
3 3532 20
4 3170 22
5 2575 28
6 3735 20
7 2605 27
8 3772 18
9 3310 19
10 2993 26
11 2755 25
Solutions
Expert Solution
Solution:
(a) Compute the coefficient of determination of the expanded data set. What effect does the addition of the twelfth car to the data set have on R-squared?
Answer: We can use the excel regression data analysis tool to find the coefficient of determination. The excel output is given below:
Therefore, the coefficient of determination is 0.4929. Addition of the twelfth car has reduced the R-squared value of the model.
(b) Is the point corresponding to the twelfth car influential? Is it an outlier?
Answer: The point corresponding to the twelfth car is an outlier.
milcah answered 1 year agoRelated Solutions
The data in the table represent the weights of various domestic cars and their miles per...
The data in the table represent the weights of various domestic
cars and their miles per gallon in the city for the 2008 model
year. For the data from the first 11 cars, the least-squares
regression line is y=−0.0062x+42.4755. A twelfth car weighs 2,705
pounds and gets 14 miles per gallon. Compute the coefficient of
determination of the expanded data set (including the twelfth
car). What effect does the addition of the twelfth car to the data
set have on...
The accompanying data represent the miles per gallon of a random sample of cars with a...
The accompanying data represent the miles per gallon of a random
sample of cars with a three-cylinder, 1.0 liter engine.
(a)
Compute the z-score corresponding to the individual who
obtained
41.4 miles per gallon. Interpret this result.
(b)
Determine the quartiles.
(c)
Compute and interpret the interquartile range, IQR.
(d)
Determine the lower and upper fences. Are there any
outliers?
32.7
34.0
34.7
35.4
36.0
36.2
37.3
37.6
37.7
37.9
38.1
38.5
38.6
39.0
39.2
39.4
39.9
40.7
41.4
41.8...
The accompanying data represent the miles per gallon of a random sample of cars with a...
The accompanying data represent the miles per gallon of a random
sample of cars with a three-cylinder, 1.0 liter engine.
(a)
Compute the z-score corresponding
to the individual who obtained
36.3
miles per gallon. Interpret this result.
(b)
Determine the quartiles.
(c)
Compute and interpret the interquartile range, IQR.
(d)
Determine the lower and upper fences. Are there any
outliers?
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32.5
35.9
38.0
38.6
39.9
42.4
34.4
36.3
38.1
38.7
40.6
42.7...
The accompanying data represent the miles per gallon of a random sample of cars with a...
The accompanying data represent the miles per gallon of a random
sample of cars with a three-cylinder, 1.0 liter engine. (a)
Compute the z-score corresponding to the individual who obtained
38.4 miles per gallon. Interpret this result. (b) Determine the
quartiles. (c) Compute and interpret the interquartile range,
IQR. (d) Determine the lower and upper fences. Are there any
outliers? 32.5; 35.9; 37.6; 38.6; 40.4; 42.5; 34.0; 36.2; 37.8;
38.9; 40.6; 42.6; 34.7; 37.3; 38.1; 39.4 ;41.3; 43.4; 35.6; 37.4;...
the accompanying data represent the miles per gallon of a random sample of cars with a...
the accompanying data represent the miles per gallon
of a random sample of cars with a three-cylinder, 1.0 liter
engine. (a) compute the z-score corresponding to the individual
who obtained 38.7 miles per gallon. interpret this result. (b)
determine the quartiles. (c) compute and interpret the
interquartile range, iqr. (d) determine the lower and upper
fences. are there any outliers?39.939.9 42.442.4 34.634.6 36.336.3
38.138.1 38.938.9 40.540.5 42.842.8 34.734.7 37.537.5 38.338.3
39.439.4 41.441.4 43.643.6 35.235.2 37.637.6 38.538.5 39.739.7
41.641.6 49.049.0
The accompanying data represent the miles per gallon of a random sample of cars with a...
The accompanying data represent the miles per gallon of a random
sample of cars with a three-cylinder, 1.0 liter engine.
(a)
Compute the z-score corresponding to the individual who
obtained
39.839.8
miles per gallon. Interpret this result.
(b)
Determine the quartiles.
(c)
Compute and interpret the interquartile range, IQR.
(d)
Determine the lower and upper fences. Are there any
outliers?
32.4
34.1
34.5
35.7
36.1
36.3
37.5
37.7
37.9
38.1
38.3
38.5
38.7
39.1
39.5
39.8
39.9
40.6
41.3
41.6...
The accompanying data represent the miles per gallon of a random sample of cars with a...
The accompanying data represent the miles per gallon of a random
sample of cars with a three-cylinder, 1.0 liter engine. (a)
Compute the z-score corresponding to the individual who obtained
32.7 miles per gallon. Interpret this result. (b) Determine the
quartiles. (c) Compute and interpret the interquartile range,
IQR. (d) Determine the lower and upper fences. Are there any
outliers?
32.7
35.9
38.0
38.7
40.2
42.2
34.4
36.2
38.1
38.9
40.7
42.7
34.6
37.5
38.2
39.5
41.5
43.6
35.2
37.8...
The following table shows the miles per gallon of various cars and their weight in pounds....
The following table shows the miles per gallon of various cars
and their weight in pounds. Suppose we are interested in predicting
the miles per gallon of a car based on its weight.
Car
Weight
MPG
Buick Lucerne
3735
17
Cadillac CTS
3860
16
Chevrolet Cobalt
2721
25
Chevrolet Impala
3555
19
Chrysler Sebring Sedan
3319
21
Dodge Caliber
2966
23
Dodge Charger
3727
17
Ford Focus
2605
24
Ford Mustang
3473
19
Lincoln MKZ
3796
17
Mercury Sable
3310...
The data in the accompanying table represent the heights and weights of a random sample of...
The data in the accompanying table represent the heights and
weights of a random sample of professional baseball players.
Complete parts (a) through (c) below.
Player Height_(inches)
Weight_(pounds)
Player_1 76 227
Player_2 75 197
Player_3 72 180
Player_4 82 231
Player_5 69 185
Player_6 74 190
Player_7 75 228
Player_8 71 200
Player_9 75 230
(b) Determine the least-squares regression line. Test whether
there is a linear relation between height and weight at the
alphaαequals=0.05
level of significance.
Determine the...
The data in the accompanying table represent the heights and weights of a random sample of...
The data in the accompanying table represent the heights and
weights of a random sample of professional baseball players.
Complete parts (a) through (c) below.
Player
Height (inches)
Weight (pounds)
Player 1
75
225
Player 2
75
197
Player 3
72
180
Player 4
82
231
Player 5
69
185
Player 6
7474
190190
Player 7
75
228
Player 8
71
200
Player 9
75
230
(a) Draw a scatter diagram of the data, treating height as the
explanatory variable...
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