Solutions to Tutorial 5 Problems

Source Sum of Squares df Mean Square F-test

Regression 2174.4 1 2174.4 40.34

Residual 862.5 16 53.9

Total 3036.9 17

ANOVA Table

Variable Coefficients s.e. T-test P-value

Constant 3.43179* 12.95 .265* .7941*

X1 .9025 .1421* 6.35 <.0001*

n=18 R^2=.716* Ra^2=.698 S=7.342* df=16

Coefficient Table

Problem 1

.9025.1421.35.6)ˆ.(.ˆ

,35.634.40

34.409.53/4.2174/

2174.4SSR/1MSR ,4.21745.8629.3036

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MSE

pn

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a

Problem 2

level. cesignifican 5%at needed

not are HS and Female variablesThe H0.reject t can' :Conclusion

3.15.)F(2,44,.05 (2,44),df

.02129[34926/44]34926)/2]/-(34959.8[F

46.df(R) 34959.8,SSE(R)

44,1-6-511-p-ndf(F) 34926,SSE(F)

0. allnot are , :H1 vs0,0 :H0 (b).

model. in the needednot likely most isit and .05,at

t significannot is Female theThus, H0.reject t Can' :Conclusion

.05.851.,19.561.5/053.1)ˆ.(./ˆ

0 :H1 vs0 :H0 (a).

Price:X6 Female:X5Black :X4

Income :X3 HS :X2 Age : X1 Sales, :Y

...Y Model

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555

55

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valuepesT

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%6.10R (f)

%3.30R (e)

%8.26R (d)

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is for CI 95% The income. :X3 (c)

2

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est

The Full Medel for (a),(b), and (c )

Results for: P081.txt

Regression Analysis: Sales versus Age, HS, Income, Black, Female, Price

The regression equation is

Sales = 103 + 4.52 Age - 0.062 HS + 0.0189 Income + 0.358 Black - 1.05 Female

- 3.25 Price

Predictor Coef SE Coef T P

Constant 103.3 245.6 0.42 0.676

Age 4.520 3.220 1.40 0.167

HS -0.0616 0.8147 -0.08 0.940

Income 0.01895 0.01022 1.85 0.070

Black 0.3575 0.4872 0.73 0.467

Female -1.053 5.561 -0.19 0.851

Price -3.255 1.031 -3.16 0.003

S = 28.17 R-Sq = 32.1% R-Sq(adj) = 22.8%

Analysis of Variance

Source DF SS MS F P

Regression 6 16499.5 2749.9 3.46 0.007

Residual Error 44 34926.0 793.8

Total 50 51425.4

The RM for (b)

Regression Analysis: Sales versus Age, Income, Black, Price

The regression equation is

Sales = 55.3 + 4.19 Age + 0.0189 Income + 0.334 Black - 3.24 Price

Predictor Coef SE Coef T P

Constant 55.33 62.40 0.89 0.380

Age 4.192 2.196 1.91 0.062

Income 0.018892 0.006882 2.75 0.009

Black 0.3342 0.3121 1.07 0.290

Price -3.2399 0.9988 -3.24 0.002

S = 27.57 R-Sq = 32.0% R-Sq(adj) = 26.1%

Analysis of Variance

Source DF SS MS F P

Regression 4 16465.7 4116.4 5.42 0.001

Residual Error 46 34959.8 760.0

Total 50 51425.4

(d)

Regression Analysis: Sales versus Age, HS, Black, Female, Price

The regression equation is

Sales = 162 + 7.31 Age + 0.972 HS + 0.845 Black - 3.78 Female - 2.86 Price

Predictor Coef SE Coef T P

Constant 162.3 250.1 0.65 0.520

Age 7.307 2.924 2.50 0.016

HS 0.9717 0.6103 1.59 0.118

Black 0.8447 0.4213 2.00 0.051

Female -3.781 5.506 -0.69 0.496

Price -2.860 1.036 -2.76 0.008

S = 28.93 R-Sq = 26.8% R-Sq(adj) = 18.6%

Analysis of Variance

Source DF SS MS F P

Regression 5 13769.3 2753.9 3.29 0.013

Residual Error 45 37656.1 836.8

Total 50 51425.4

(e)

Regression Analysis: Sales versus Age, Income, Price

The regression equation is

Sales = 64.2 + 4.16 Age + 0.0193 Income - 3.40 Price

Predictor Coef SE Coef T P

Constant 64.25 61.93 1.04 0.305

Age 4.156 2.199 1.89 0.065

Income 0.019281 0.006883 2.80 0.007

Price -3.3992 0.9892 -3.44 0.001

S = 27.61 R-Sq = 30.3% R-Sq(adj) = 25.9%

Analysis of Variance

Source DF SS MS F P

Regression 3 15594.4 5198.1 6.82 0.001

Residual Error 47 35831.0 762.4

Total 50 51425.4

(f)

Regression Analysis: Sales versus Income

The regression equation is

Sales = 55.4 + 0.0176 Income

Predictor Coef SE Coef T P

Constant 55.36 27.74 2.00 0.052

Income 0.017583 0.007283 2.41 0.020

S = 30.63 R-Sq = 10.6% R-Sq(adj) = 8.8%

Analysis of Variance

Source DF SS MS F P

Regression 1 5467.6 5467.6 5.83 0.020

Residual Error 49 45957.9 937.9

Total 50 51425.4