Inference for the Least-Squares Line
Content
AP Statistics
Assignment: Inference for the Least-Squares Line
Page 1 of 4
1. The following data set contains the number of seats and the average flight-length for 17
aircraft. This data appeared in Contemporary Precalculus with Applications, by the North
Carolina School of Science and Mathematics, published in 2000 by Everyday Learning
Corporation, Chicago, IL.
Aircraft
Number of Seats
B747-100
405
L-1011-100/200
296
DC-10-10
288
A300 B4
258
A310-300
240
B767-300
230
B767-200
193
B757-200
188
B727-200
148
MD-80
142
B737-300
131
DC-9-50
122
B727-100
115
B737-100/200
112
F-100
103
DC-9-30
102
DC-9-10
78
Flight Length (mi)
3,149
1,631
1,410
1,221
1,512
1,668
1,736
984
688
667
605
685
626
440
384
421
394
A. Using your JUDSKLQJ calculator, construct a least-squares regression line for
WKHVHdata. (2 points)
B. Is the linear model appropriate for these data? Explain. (2 points)
C. State your hypotheses for a two-sided significance test of the slope of the
regression line. (1 point)
D. Use your JUDSKLQJ calculator to find the test statistic and P-value for this
significance test. (2 points)
E. Draw a conclusion based on t = 9.9067 and p = .0000000565 for the
significance test H0 : β 1 = 0, H a : β 1 ≠ 0 with α = .01. (1 point)
F. Calculate the standard error of the slope of the regression line. (2 points)
G. Construct a 99% confidence interval for the slope of the regression line.
(2 points)
H. Interpret the confidence interval (5.32, 9.82) for the slope of the regression
line. (1 point)
______________________________
Copyright © 2011 Apex Learning Inc. (See Terms of Use at www.apexvs.com/TermsOfUse)
AP Statistics
Assignment: Inference for the Least-Squares Line
Page 2 of 4
2. Can we predict the average January temperature of a city in the U.S. based on its
latitude? The following data were collected on U.S. cities (data is from DASL collection,
noted for free use):
City
Jan. Temp
Mobile, AL
44
Montgomery, AL
38
Phoenix, AZ
35
Little Rock, AR
31
Los Angeles, CA
47
San Francisco, CA
42
Denver, CO
15
New Haven, CT
22
Wilmington, DE
26
Washington, DC
30
Jacksonville, FL
45
Key West, FL
65
Miami, FL
58
Atlanta, GA
37
Boise, ID
22
Chicago, IL
19
Indianapolis, IN
21
Des Moines, IA
11
Wichita, KS
22
Louisville, KY
27
New Orleans, LA
45
Portland, ME
12
Baltimore, MD
25
Boston, MA
23
Detroit, MI
21
Minneapolis, MN
2
St. Louis, MO
24
Helena, MT
8
Omaha, NE
13
Concord, NH
11
Atlantic City, N
27
Albuquerque, NM
24
Albany, NY
14
New York, NY
27
Charlotte, NC
34
Raleigh, NC
31
Bismarck, ND
0
Cincinnati, OH
26
Cleveland, OH
21
Oklahoma City, OK
28
Portland, OR
33
Harrisburg, PA
24
Philadelphia, PA
24
Lat
31.2
32.9
33.6
35.4
34.3
38.4
40.7
41.7
40.5
39.7
31
25
26.3
33.9
43.7
42.3
39.8
41.8
38.1
39
30.8
44.2
39.7
42.7
43.1
45.9
39.3
47.1
41.9
43.5
39.8
35.1
42.6
40.8
35.9
36.4
47.1
39.2
42.3
35.9
45.6
40.9
40.9
______________________________
Copyright © 2011 Apex Learning Inc. (See Terms of Use at www.apexvs.com/TermsOfUse)
Page 3 of 4
AP Statistics
Assignment: Inference for the Least-Squares Line
Charleston, SC
Nashville, TN
Amarillo, TX
Galveston, TX
Houston, TX
Salt Lake City, UT
Burlington, VT
Norfolk, VA
Seattle, WA
Spokane, WA
Madison, WI
Milwaukee, WI
Cheyenne, WY
38
31
24
49
44
18
7
32
33
19
9
13
14
33.3
36.7
35.6
29.4
30.1
41.1
45
37
48.1
48.1
43.4
43.3
41.2
The following is computer output from a regression analysis:
Dependent variable is:
Av. Jan. Temp.
No Selector
57 total cases of which 1 is missing
R squared = 71.9%
R squared (adjusted) = 71.4%
s = 7.156 with 56 – 2 = 54 degrees of freedom
Source
Regression
Sum of Squares
7080.87
df
1
Residual
2765.11
54
Mean Square
7080.87
F-ratio
138
51.2057
Variable
Constant
Coefficient
108.728
s.e. of Coeff
7.056
t-ratio
15.4
prob
< 0.0001
Latitude
–2.10959
0.1794
–11.8
< 0.0001
A. Construct the linear regression equation for predicting average January
temperature from latitude. (2 points)
B. Use this equation to predict the average January temperature of a city at 63
degrees latitude. Is this an appropriate use of this regression equation?
Explain. (2 points)
C. Use this equation to predict the average January temperature of a city at 45
degrees latitude. Is this an appropriate use of this regression equation?
Explain. (2 points)
D. What's the test statistic and P-value for a two-sided significance test of the
slope of this regression line? (1 point)
E. Draw a conclusion based on this P-value for the significance test H0 : β 1 = 0
and H a : β 1 ≠ 0, with α = .05. (1 point)
______________________________
Copyright © 2011 Apex Learning Inc. (See Terms of Use at www.apexvs.com/TermsOfUse)
AP Statistics
Assignment: Inference for the Least-Squares Line
Page 4 of 4
F. Construct a 95% confidence interval for the slope of this regression line.
(Hint To find t
for a value that doesn't appear in your table, use 7,QWHUYDO
LQWKHSTAT TESTS menu. Note that your calculator expects you to enter QWKHQ
calculates df = n – 1. For this problem, however, your degrees of freedom
QHHGto equal n – 2. How do you think you can work around this?)
G. Interpret the confidence interval (–2.469, –1.7499) for the slope of the
regression line. (2 points)
______________________________
Copyright © 2011 Apex Learning Inc. (See Terms of Use at www.apexvs.com/TermsOfUse)
Assignment: Inference for the Least-Squares Line
Page 1 of 4
1. The following data set contains the number of seats and the average flight-length for 17
aircraft. This data appeared in Contemporary Precalculus with Applications, by the North
Carolina School of Science and Mathematics, published in 2000 by Everyday Learning
Corporation, Chicago, IL.
Aircraft
Number of Seats
B747-100
405
L-1011-100/200
296
DC-10-10
288
A300 B4
258
A310-300
240
B767-300
230
B767-200
193
B757-200
188
B727-200
148
MD-80
142
B737-300
131
DC-9-50
122
B727-100
115
B737-100/200
112
F-100
103
DC-9-30
102
DC-9-10
78
Flight Length (mi)
3,149
1,631
1,410
1,221
1,512
1,668
1,736
984
688
667
605
685
626
440
384
421
394
A. Using your JUDSKLQJ calculator, construct a least-squares regression line for
WKHVHdata. (2 points)
B. Is the linear model appropriate for these data? Explain. (2 points)
C. State your hypotheses for a two-sided significance test of the slope of the
regression line. (1 point)
D. Use your JUDSKLQJ calculator to find the test statistic and P-value for this
significance test. (2 points)
E. Draw a conclusion based on t = 9.9067 and p = .0000000565 for the
significance test H0 : β 1 = 0, H a : β 1 ≠ 0 with α = .01. (1 point)
F. Calculate the standard error of the slope of the regression line. (2 points)
G. Construct a 99% confidence interval for the slope of the regression line.
(2 points)
H. Interpret the confidence interval (5.32, 9.82) for the slope of the regression
line. (1 point)
______________________________
Copyright © 2011 Apex Learning Inc. (See Terms of Use at www.apexvs.com/TermsOfUse)
AP Statistics
Assignment: Inference for the Least-Squares Line
Page 2 of 4
2. Can we predict the average January temperature of a city in the U.S. based on its
latitude? The following data were collected on U.S. cities (data is from DASL collection,
noted for free use):
City
Jan. Temp
Mobile, AL
44
Montgomery, AL
38
Phoenix, AZ
35
Little Rock, AR
31
Los Angeles, CA
47
San Francisco, CA
42
Denver, CO
15
New Haven, CT
22
Wilmington, DE
26
Washington, DC
30
Jacksonville, FL
45
Key West, FL
65
Miami, FL
58
Atlanta, GA
37
Boise, ID
22
Chicago, IL
19
Indianapolis, IN
21
Des Moines, IA
11
Wichita, KS
22
Louisville, KY
27
New Orleans, LA
45
Portland, ME
12
Baltimore, MD
25
Boston, MA
23
Detroit, MI
21
Minneapolis, MN
2
St. Louis, MO
24
Helena, MT
8
Omaha, NE
13
Concord, NH
11
Atlantic City, N
27
Albuquerque, NM
24
Albany, NY
14
New York, NY
27
Charlotte, NC
34
Raleigh, NC
31
Bismarck, ND
0
Cincinnati, OH
26
Cleveland, OH
21
Oklahoma City, OK
28
Portland, OR
33
Harrisburg, PA
24
Philadelphia, PA
24
Lat
31.2
32.9
33.6
35.4
34.3
38.4
40.7
41.7
40.5
39.7
31
25
26.3
33.9
43.7
42.3
39.8
41.8
38.1
39
30.8
44.2
39.7
42.7
43.1
45.9
39.3
47.1
41.9
43.5
39.8
35.1
42.6
40.8
35.9
36.4
47.1
39.2
42.3
35.9
45.6
40.9
40.9
______________________________
Copyright © 2011 Apex Learning Inc. (See Terms of Use at www.apexvs.com/TermsOfUse)
Page 3 of 4
AP Statistics
Assignment: Inference for the Least-Squares Line
Charleston, SC
Nashville, TN
Amarillo, TX
Galveston, TX
Houston, TX
Salt Lake City, UT
Burlington, VT
Norfolk, VA
Seattle, WA
Spokane, WA
Madison, WI
Milwaukee, WI
Cheyenne, WY
38
31
24
49
44
18
7
32
33
19
9
13
14
33.3
36.7
35.6
29.4
30.1
41.1
45
37
48.1
48.1
43.4
43.3
41.2
The following is computer output from a regression analysis:
Dependent variable is:
Av. Jan. Temp.
No Selector
57 total cases of which 1 is missing
R squared = 71.9%
R squared (adjusted) = 71.4%
s = 7.156 with 56 – 2 = 54 degrees of freedom
Source
Regression
Sum of Squares
7080.87
df
1
Residual
2765.11
54
Mean Square
7080.87
F-ratio
138
51.2057
Variable
Constant
Coefficient
108.728
s.e. of Coeff
7.056
t-ratio
15.4
prob
< 0.0001
Latitude
–2.10959
0.1794
–11.8
< 0.0001
A. Construct the linear regression equation for predicting average January
temperature from latitude. (2 points)
B. Use this equation to predict the average January temperature of a city at 63
degrees latitude. Is this an appropriate use of this regression equation?
Explain. (2 points)
C. Use this equation to predict the average January temperature of a city at 45
degrees latitude. Is this an appropriate use of this regression equation?
Explain. (2 points)
D. What's the test statistic and P-value for a two-sided significance test of the
slope of this regression line? (1 point)
E. Draw a conclusion based on this P-value for the significance test H0 : β 1 = 0
and H a : β 1 ≠ 0, with α = .05. (1 point)
______________________________
Copyright © 2011 Apex Learning Inc. (See Terms of Use at www.apexvs.com/TermsOfUse)
AP Statistics
Assignment: Inference for the Least-Squares Line
Page 4 of 4
F. Construct a 95% confidence interval for the slope of this regression line.
(Hint To find t
for a value that doesn't appear in your table, use 7,QWHUYDO
LQWKHSTAT TESTS menu. Note that your calculator expects you to enter QWKHQ
calculates df = n – 1. For this problem, however, your degrees of freedom
QHHGto equal n – 2. How do you think you can work around this?)
G. Interpret the confidence interval (–2.469, –1.7499) for the slope of the
regression line. (2 points)
______________________________
Copyright © 2011 Apex Learning Inc. (See Terms of Use at www.apexvs.com/TermsOfUse)
