Use Minitab , R, or your preferred software for this question, but calculate the
ID: 3219310 • Letter: U
Question
Use Minitab, R, or your preferred software for this question, but calculate the 90% confidence interval for the coefficient for cable by hand (but use the SE from the software output) and do the test whether age and number of TVs should be dropped by hand (but use the ANVOA tables from software).
The data in the table below contains observations on age, sex (male = 0, female = 1), number of television sets in the household, cable (no = 0, yes = 1), and number of hours of television watched per week. Using hours of television watched per week as the response, you can use Minitab's Regress or R's lm() command [e.g., model <- lm(hours~age+sex+num.tv+cable)] to fit a least squares regression model to all the other given variables.
The estimated value of the regression coefficient for age= 0.1000
The estimated value of the regression coefficient for cable= 4.1980
The value of the test-statistic for the overall regression significance test is 12.6200
[Compute a 90% confidence interval for the coefficient for cable. Lower Bound: Upper Bound: [3 pt(s)]
Compute a 95% confidence interval for the mean number of hours watched by 18-year old females with cable and 2 TV sets. Lower Bound: Upper Bound: [3 pt(s)]
Compute a 95% prediction interval for the mean number of hours watched by 18-year old females with cable and 2 TV sets. Lower Bound: Upper Bound: [3 pt(s)]
Test whether age and number of TV sets are needed in the model or should be dropped. What is the value of the test-statistic? [3 pt(s)]
What are the degrees of freedom associated with this test? Numerator: Denominator: [1 pt(s)]
Select the interval below that contains the p-value for this test.
p-value 0.001
0.001 < p-value 0.01
0.01 < p-value 0.05
0.05 < p-value 0.1
0.1 < p-value 0.25
p-value > 0.25
[3 pt(s)]
Explanation / Answer
The estimated value of the regression coefficient for age= 0.1000
The estimated value of the regression coefficient for cable= 4.1980
The Minitab output is shown below:
Regression Analysis: HoursTV versus Age, Sex, Num. TV, Cable
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 4 571.270 142.817 12.62 0.000
Age 1 45.259 45.259 4.00 0.053
Sex 1 115.765 115.765 10.23 0.003
Num. TV 1 6.375 6.375 0.56 0.458
Cable 1 134.331 134.331 11.87 0.001
Error 35 396.105 11.317
Lack-of-Fit 34 395.605 11.635 23.27 0.163
Pure Error 1 0.500 0.500
Total 39 967.375
Model Summary
S R-sq R-sq(adj) R-sq(pred)
3.36412 59.05% 54.37% 43.29%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 11.67 2.31 5.05 0.000
Age 0.1000 0.0500 2.00 0.053 1.25
Sex -3.58 1.12 -3.20 0.003 1.09
Num. TV 0.86 1.14 0.75 0.458 1.05
Cable 4.20 1.22 3.45 0.001 1.31
Regression Equation
HoursTV = 11.67 + 0.1000 Age - 3.58 Sex + 0.86 Num. TV + 4.20 Cable
Fits and Diagnostics for Unusual Observations
Obs HoursTV Fit Resid Std Resid
1 28.00 19.78 8.22 2.61 R
11 15.00 23.38 -8.38 -2.87 R
R Large residual
Coefficients
Term Coef SE Coef 90% CI T-Value P-Value VIF
Constant 11.67 2.31 ( 7.77, 15.57) 5.05 0.000
Age 0.1000 0.0500 (0.0155, 0.1845) 2.00 0.053 1.25
Sex -3.58 1.12 ( -5.47, -1.69) -3.20 0.003 1.09
Num. TV 0.86 1.14 ( -1.07, 2.79) 0.75 0.458 1.05
Cable 4.20 1.22 ( 2.14, 6.26) 3.45 0.001 1.31
Coefficients
Term Coef SE Coef 95% CI T-Value P-Value VIF
Constant 11.67 2.31 ( 6.98, 16.35) 5.05 0.000
Age 0.1000 0.0500 (-0.0015, 0.2015) 2.00 0.053 1.25
Sex -3.58 1.12 ( -5.85, -1.31) -3.20 0.003 1.09
Num. TV 0.86 1.14 ( -1.46, 3.18) 0.75 0.458 1.05
Cable 4.20 1.22 ( 1.72, 6.67) 3.45 0.001 1.31
The value of the test-statistic for the overall regression significance test is 12.6200
What are the degrees of freedom associated with the test-statistic?
Numerator: 4
Denominator: 35
[Compute a 90% confidence interval for the coefficient for cable.
Lower Bound: 2.14
Upper Bound: 6.26
Compute a 95% confidence interval for the mean number of hours watched by 18-year old females with cable and 2 TV sets.
Prediction for HoursTV
Regression Equation
HoursTV = 11.67 + 0.1000 Age - 3.58 Sex + 0.86 Num. TV + 4.20 Cable
Variable Setting
Age 18
Sex 1
Num. TV 2
Cable 1
Fit SE Fit 95% CI 95% PI
15.8056 1.41557 (12.9318, 18.6793) (8.39604, 23.2151)
Lower Bound: 12.9318
Upper Bound: 18.6793
Compute a 95% prediction interval for the mean number of hours watched by 18-year old females with cable and 2 TV sets.
Lower Bound: 8.39604
Upper Bound: 23.2151
Test whether age and number of TV sets are needed in the model or should be dropped. What is the value of the test-statistic?
For Age, t=2.00 and for number of TV sets, t=0.75. p-value for both are greater than 0.05, age and number of TV sets in the model should be dropped.
Regression Analysis: HoursTV versus Sex, Cable
Analysis of Variance
Source DF Seq SS Contribution Adj SS Adj MS F-Value P-Value
Regression 2 522.39 54.00% 522.39 261.19 21.72 0.000
Sex 1 260.16 26.89% 135.47 135.47 11.26 0.002
Cable 1 262.23 27.11% 262.23 262.23 21.80 0.000
Error 37 444.99 46.00% 444.99 12.03
Lack-of-Fit 1 30.93 3.20% 30.93 30.93 2.69 0.110
Pure Error 36 414.06 42.80% 414.06 11.50
Total 39 967.38 100.00%
Model Summary
S R-sq R-sq(adj) PRESS R-sq(pred)
3.46795 54.00% 51.51% 524.393 45.79%
Coefficients
Term Coef SE Coef 90% CI T-Value P-Value VIF
Constant 15.21 1.07 (13.40, 17.02) 14.20 0.000
Sex -3.82 1.14 (-5.74, -1.90) -3.36 0.002 1.06
Cable 5.29 1.13 ( 3.38, 7.20) 4.67 0.000 1.06
Regression Equation
HoursTV = 15.21 - 3.82 Sex + 5.29 Cable
Fits and Diagnostics for Unusual Observations
Std Del
Obs HoursTV Fit SE Fit 90% CI Resid Resid Resid HI Cook’s D DFITS
1 28.000 20.502 0.929 (18.935, 22.069) 7.498 2.24 2.38 0.0716981 0.13 0.661856 R
R Large residual
What are the degrees of freedom associated with this test?
Numerator: 2
Denominator: 37
Select the interval below that contains the p-value for this test.
p-value 0.001
The Minitab output is shown below:
Regression Analysis: HoursTV versus Age, Sex, Num. TV, Cable
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 4 571.270 142.817 12.62 0.000
Age 1 45.259 45.259 4.00 0.053
Sex 1 115.765 115.765 10.23 0.003
Num. TV 1 6.375 6.375 0.56 0.458
Cable 1 134.331 134.331 11.87 0.001
Error 35 396.105 11.317
Lack-of-Fit 34 395.605 11.635 23.27 0.163
Pure Error 1 0.500 0.500
Total 39 967.375
Model Summary
S R-sq R-sq(adj) R-sq(pred)
3.36412 59.05% 54.37% 43.29%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 11.67 2.31 5.05 0.000
Age 0.1000 0.0500 2.00 0.053 1.25
Sex -3.58 1.12 -3.20 0.003 1.09
Num. TV 0.86 1.14 0.75 0.458 1.05
Cable 4.20 1.22 3.45 0.001 1.31
Regression Equation
HoursTV = 11.67 + 0.1000 Age - 3.58 Sex + 0.86 Num. TV + 4.20 Cable
Fits and Diagnostics for Unusual Observations
Obs HoursTV Fit Resid Std Resid
1 28.00 19.78 8.22 2.61 R
11 15.00 23.38 -8.38 -2.87 R
R Large residual
Coefficients
Term Coef SE Coef 90% CI T-Value P-Value VIF
Constant 11.67 2.31 ( 7.77, 15.57) 5.05 0.000
Age 0.1000 0.0500 (0.0155, 0.1845) 2.00 0.053 1.25
Sex -3.58 1.12 ( -5.47, -1.69) -3.20 0.003 1.09
Num. TV 0.86 1.14 ( -1.07, 2.79) 0.75 0.458 1.05
Cable 4.20 1.22 ( 2.14, 6.26) 3.45 0.001 1.31
Coefficients
Term Coef SE Coef 95% CI T-Value P-Value VIF
Constant 11.67 2.31 ( 6.98, 16.35) 5.05 0.000
Age 0.1000 0.0500 (-0.0015, 0.2015) 2.00 0.053 1.25
Sex -3.58 1.12 ( -5.85, -1.31) -3.20 0.003 1.09
Num. TV 0.86 1.14 ( -1.46, 3.18) 0.75 0.458 1.05
Cable 4.20 1.22 ( 1.72, 6.67) 3.45 0.001 1.31
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