> vy=var (y) > vz=var (z) > c(vx, vy, vz) [1] 144418.27 225582.61 14015.52 > > reg=1m (y^x) > summary(reg) Call: 1m (formula = y x) Residuals: Min -147.179 1Q Median 3Q Max -77.542 -8.385 53.611 239.163 Coefficients: Estimate Std. Error t value Pr(>|t|) 102.16744 -0.70 0.09589 (Intercept) -71.51136 1.21246 0.5 12.64 1.78e-07 *** Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 1 Residual standard error: 120.9 on 10 degrees of freedom Adjusted R-squared: 0.9352 Multiple R-squared: 0.9411, F-statistic: 159.9 on 1 and 10 DF, p-value: 1.784e-07 > mse=sum(reg $residuals^2)/10 > mse [1] 14606.97 (a) Estimate using the sample mean . (b) Estimate using the ratio estimator. (c) Estimate using the regression estimator. (d) Compute the (approximate) relative efficiency of the ratio estimator with respect to the regression estimator. 3. A corporation is interested in estimating the mean earnings from sales of color television sets at the end of a three-month period. The total earnings figures are available for all districts within the corporation for the corresponding three-month period of the previous year. A simple random sample of 12 district offices is selected from 123 offices within the corporation. Use the data in the accompanying table to estimate the mean earnings for offices within the corporation and place a bound on the error of estimation. Take Tx = 128,200. Office 1 Previous year xi Current year yi 550 610 2 720 780 3 1500 1600 4 1020 1030 5 620 600 6 980 1050 7 928 977 8 1200 1440 9 1350 1570 10 1750 2210 11 670 980 12 729 865 You may find the following R codes and outputs helpful. > x=c (550,720, 1500, 1020,620,980,928,1200,1350,1750,670,729) > y=c(610,780, 1600, 1030, 600, 1050,977, 1440, 1570, 2210,980,865) > > f=1-12/123 > mux=128200/123 > c(f,mux) [1] 0.902439 1042.276423 > mx=mean(x) > my=mean(y) > r=my/mx > z=y-r*x > mz=mean (z) > c(mx, my, mz,r) [1] 1.001417e+03 > vx=var(x) 1.142667e+03 -8.526513e-14 1.141050e+00
> vy=var (y) > vz=var (z) > c(vx, vy, vz) [1] 144418.27 225582.61 14015.52 > > reg=1m (y^x) > summary(reg) Call: 1m (formula = y x) Residuals: Min -147.179 1Q Median 3Q Max -77.542 -8.385 53.611 239.163 Coefficients: Estimate Std. Error t value Pr(>|t|) 102.16744 -0.70 0.09589 (Intercept) -71.51136 1.21246 0.5 12.64 1.78e-07 *** Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 1 Residual standard error: 120.9 on 10 degrees of freedom Adjusted R-squared: 0.9352 Multiple R-squared: 0.9411, F-statistic: 159.9 on 1 and 10 DF, p-value: 1.784e-07 > mse=sum(reg $residuals^2)/10 > mse [1] 14606.97 (a) Estimate using the sample mean . (b) Estimate using the ratio estimator. (c) Estimate using the regression estimator. (d) Compute the (approximate) relative efficiency of the ratio estimator with respect to the regression estimator. 3. A corporation is interested in estimating the mean earnings from sales of color television sets at the end of a three-month period. The total earnings figures are available for all districts within the corporation for the corresponding three-month period of the previous year. A simple random sample of 12 district offices is selected from 123 offices within the corporation. Use the data in the accompanying table to estimate the mean earnings for offices within the corporation and place a bound on the error of estimation. Take Tx = 128,200. Office 1 Previous year xi Current year yi 550 610 2 720 780 3 1500 1600 4 1020 1030 5 620 600 6 980 1050 7 928 977 8 1200 1440 9 1350 1570 10 1750 2210 11 670 980 12 729 865 You may find the following R codes and outputs helpful. > x=c (550,720, 1500, 1020,620,980,928,1200,1350,1750,670,729) > y=c(610,780, 1600, 1030, 600, 1050,977, 1440, 1570, 2210,980,865) > > f=1-12/123 > mux=128200/123 > c(f,mux) [1] 0.902439 1042.276423 > mx=mean(x) > my=mean(y) > r=my/mx > z=y-r*x > mz=mean (z) > c(mx, my, mz,r) [1] 1.001417e+03 > vx=var(x) 1.142667e+03 -8.526513e-14 1.141050e+00
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 1GP
Related questions
Question
![> vy=var (y)
> vz=var (z)
> c(vx, vy, vz)
[1] 144418.27 225582.61 14015.52
>
> reg=1m (y^x)
> summary(reg)
Call:
1m (formula = y x)
Residuals:
Min
-147.179
1Q Median
3Q
Max
-77.542 -8.385 53.611 239.163
Coefficients:
Estimate Std. Error t value Pr(>|t|)
102.16744 -0.70
0.09589
(Intercept) -71.51136
1.21246
0.5
12.64 1.78e-07 ***
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 1
Residual standard error: 120.9 on 10 degrees of freedom
Adjusted R-squared: 0.9352
Multiple R-squared:
0.9411,
F-statistic: 159.9 on 1 and 10 DF, p-value: 1.784e-07
> mse=sum(reg $residuals^2)/10
> mse
[1] 14606.97
(a) Estimate using the sample mean .
(b) Estimate using the ratio estimator.
(c) Estimate using the regression estimator.
(d) Compute the (approximate) relative efficiency of the ratio estimator
with respect to the regression estimator.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F008f8cce-1e45-43a4-8b17-46721d7357f5%2F7a5e9da7-311b-4efa-b28b-b4a9ed1f391d%2Fpy6286_processed.png&w=3840&q=75)
Transcribed Image Text:> vy=var (y)
> vz=var (z)
> c(vx, vy, vz)
[1] 144418.27 225582.61 14015.52
>
> reg=1m (y^x)
> summary(reg)
Call:
1m (formula = y x)
Residuals:
Min
-147.179
1Q Median
3Q
Max
-77.542 -8.385 53.611 239.163
Coefficients:
Estimate Std. Error t value Pr(>|t|)
102.16744 -0.70
0.09589
(Intercept) -71.51136
1.21246
0.5
12.64 1.78e-07 ***
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 1
Residual standard error: 120.9 on 10 degrees of freedom
Adjusted R-squared: 0.9352
Multiple R-squared:
0.9411,
F-statistic: 159.9 on 1 and 10 DF, p-value: 1.784e-07
> mse=sum(reg $residuals^2)/10
> mse
[1] 14606.97
(a) Estimate using the sample mean .
(b) Estimate using the ratio estimator.
(c) Estimate using the regression estimator.
(d) Compute the (approximate) relative efficiency of the ratio estimator
with respect to the regression estimator.
![3. A corporation is interested in estimating the mean earnings from sales
of color television sets at the end of a three-month period. The total
earnings figures are available for all districts within the corporation for
the corresponding three-month period of the previous year. A simple
random sample of 12 district offices is selected from 123 offices within the
corporation. Use the data in the accompanying table to estimate the mean
earnings for offices within the corporation and place a bound on the error
of estimation. Take Tx = 128,200.
Office
1
Previous year xi
Current year yi
550
610
2
720
780
3
1500
1600
4
1020
1030
5
620
600
6
980
1050
7
928
977
8
1200
1440
9
1350
1570
10
1750
2210
11
670
980
12
729
865
You may find the following R codes and outputs helpful.
> x=c (550,720, 1500, 1020,620,980,928,1200,1350,1750,670,729)
> y=c(610,780, 1600, 1030, 600, 1050,977, 1440, 1570, 2210,980,865)
>
> f=1-12/123
> mux=128200/123
> c(f,mux)
[1]
0.902439 1042.276423
> mx=mean(x)
> my=mean(y)
> r=my/mx
> z=y-r*x
> mz=mean (z)
> c(mx, my, mz,r)
[1]
1.001417e+03
> vx=var(x)
1.142667e+03 -8.526513e-14 1.141050e+00](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F008f8cce-1e45-43a4-8b17-46721d7357f5%2F7a5e9da7-311b-4efa-b28b-b4a9ed1f391d%2F1e98yq_processed.png&w=3840&q=75)
Transcribed Image Text:3. A corporation is interested in estimating the mean earnings from sales
of color television sets at the end of a three-month period. The total
earnings figures are available for all districts within the corporation for
the corresponding three-month period of the previous year. A simple
random sample of 12 district offices is selected from 123 offices within the
corporation. Use the data in the accompanying table to estimate the mean
earnings for offices within the corporation and place a bound on the error
of estimation. Take Tx = 128,200.
Office
1
Previous year xi
Current year yi
550
610
2
720
780
3
1500
1600
4
1020
1030
5
620
600
6
980
1050
7
928
977
8
1200
1440
9
1350
1570
10
1750
2210
11
670
980
12
729
865
You may find the following R codes and outputs helpful.
> x=c (550,720, 1500, 1020,620,980,928,1200,1350,1750,670,729)
> y=c(610,780, 1600, 1030, 600, 1050,977, 1440, 1570, 2210,980,865)
>
> f=1-12/123
> mux=128200/123
> c(f,mux)
[1]
0.902439 1042.276423
> mx=mean(x)
> my=mean(y)
> r=my/mx
> z=y-r*x
> mz=mean (z)
> c(mx, my, mz,r)
[1]
1.001417e+03
> vx=var(x)
1.142667e+03 -8.526513e-14 1.141050e+00
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps
Recommended textbooks for you
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt