Question
In: Statistics and Probability
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 Rsquared2?
Car Weight_(pounds)_x
Miles_per_Gallon_y
1 3765 21
2 3980 19
3 3532 22
4 3174 21
5 2582 27
6 3729 18
7 2601 26
8 3775 18
9 3313 19
10 2991 26
11 2753 26
12 2705 14
1) The coefficient of determination of the expanded data set is
2)How does the addition of the twelfth car to the data set affect Rsquared2? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a) It increases by __
b) It decreases by __
c) it does not affect it
Solutions
Expert Solution
Solution: We can use the excel regression data analysis tool to find the answer to the given questions. The excel output is given below:
| SUMMARY OUTPUT | ||||||
| Regression Statistics | ||||||
| Multiple R | 0.4988 | |||||
| R Square | 0.2488 | |||||
| Adjusted R Square | 0.1737 | |||||
| Standard Error | 3.7269 | |||||
| Observations | 12 | |||||
| ANOVA | ||||||
| df | SS | MS | F | Significance F | ||
| Regression | 1 | 46.01604742 | 46.01604742 | 3.312875614 | 0.098755827 | |
| Residual | 10 | 138.9006192 | 13.89006192 | |||
| Total | 11 | 184.9166667 | ||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | |
| Intercept | 34.3965 | 7.2120 | 4.7694 | 0.0008 | 18.3272 | 50.4658 |
| Weight_(pounds)_x | -0.0040 | 0.0022 | -1.8201 | 0.0988 | -0.0089 | 0.0009 |
1) The coefficient of determination of the expanded data set is
Answer: 
2)How does the addition of the twelfth car to the data set affect Rsquared2? Select the correct choice below and, ifnecessary, fill in the answer box to complete your choice.
b) It decreases by 0.5365
Explanation:
R-square for 11 pairs of data set is 0.7853 and the R-square for the 12 pairs of data set is 0.2488. Therefore, the R-square is decreased by 0.7853-0.2488=0.5365
orchestra 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 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)...
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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