The data in the table represent the weights of various domestic cars and their m
ID: 3176361 • Letter: T
Question
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
ModifyingAbove y with caretyequals=negative 0.00510.0051xplus+38.892938.8929.
A twelfth car weighs
2 comma 8242,824
pounds and gets
2626
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?
LOADING...
Click the icon to view the data table.
Car Weight_(pounds)_x Miles_per_Gallon_y
1 3763 19
2 3986 20
3 3534 22
4 3171 23
5 2575 26
6 3740 19
7 2606 25
8 3780 19
9 3314 19
10 2992 25
11 2755 25
12 2824 26
The coefficient of determination of the expanded data set is
Rsquared2equals=nothing%.
(Round to one decimal place as needed.)
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
reducereduces
Rsquared2
by
nothing%.
(Round to one decimal place as needed.)
B.
It
increaseincreases
Rsquared2
by
nothing%.
(Round to one decimal place as needed.)
C.
It does not affect
Rsquared2
Explanation / Answer
Result:
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
ModifyingAbove y with caretyequals=negative 0.00510.0051xplus+38.892938.8929.
A twelfth car weighs2,824 pounds and gets 26 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?
LOADING...
Click the icon to view the data table.
Car Weight_(pounds)_x Miles_per_Gallon_y
1 3763 19
2 3986 20
3 3534 22
4 3171 23
5 2575 26
6 3740 19
7 2606 25
8 3780 19
9 3314 19
10 2992 25
11 2755 25
12 2824 26
The coefficient of determination of the expanded data set is
Rsquared2 =81.5%.
(Round to one decimal place as needed.)
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.
Answer: B.
It increase increases Rsquared2 by 0.7 %.
(Round to one decimal place as needed.)
Regression for expanded data
Regression Analysis
r²
0.8148
n
12
r
-0.9027
k
1
Std. Error
1.352
Dep. Var.
miles
ANOVA table
Source
SS
df
MS
F
p-value
Regression
80.3958
1
80.3958
44.00
.0001
Residual
18.2709
10
1.8271
Total
98.6667
11
Regression output
confidence interval
variables
coefficients
std. error
t (df=10)
p-value
95% lower
95% upper
Intercept
39.8282
2.6661
14.939
3.64E-08
33.8878
45.7687
weight
-0.0054
0.0008
-6.633
.0001
-0.0072
-0.0036
Regression for 11 cases
Regression Analysis
r²
0.8083
n
11
r
-0.8991
k
1
Std. Error
1.338
Dep. Var.
miles
ANOVA table
Source
SS
df
MS
F
p-value
Regression
67.8975
1
67.8975
37.95
.0002
Residual
16.1025
9
1.7892
Total
84.0000
10
Regression output
confidence interval
variables
coefficients
std. error
t (df=9)
p-value
95% lower
95% upper
Intercept
38.8929
2.7717
14.032
2.01E-07
32.6228
45.1629
weight
-0.0051
0.0008
-6.160
.0002
-0.0070
-0.0032
Regression Analysis
r²
0.8148
n
12
r
-0.9027
k
1
Std. Error
1.352
Dep. Var.
miles
ANOVA table
Source
SS
df
MS
F
p-value
Regression
80.3958
1
80.3958
44.00
.0001
Residual
18.2709
10
1.8271
Total
98.6667
11
Regression output
confidence interval
variables
coefficients
std. error
t (df=10)
p-value
95% lower
95% upper
Intercept
39.8282
2.6661
14.939
3.64E-08
33.8878
45.7687
weight
-0.0054
0.0008
-6.633
.0001
-0.0072
-0.0036
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