Linear Regression Results quiz 9 The REG Procedure Model: Linear_Regression_Mode

Question

Linear Regression Results quiz 9

The REG Procedure

Model: Linear_Regression_Model

Dependent Variable: Y

Number of Observations Read

31

Number of Observations Used

31

Analysis of Variance

Source

DF

Sum of
Squares

Mean
Square

F Value

Pr > F

Model

2

59753

29876

49.80

<.0001

Error

28

16799

599.94742

Corrected Total

30

76551

Root MSE

24.49382

R-Square

0.7806

Dependent Mean

133.77419

Adj R-Sq

0.7649

Coeff Var

18.30983

Parameter Estimates

Variable

DF

Parameter
Estimate

Standard
Error

t Value

Pr > |t|

95% Confidence Limits

Intercept

1

28.72150

19.24888

1.49

0.1469

-10.70803

68.15104

X1

1

1.72216

0.17259

9.98

<.0001

1.36863

2.07569

X2

1

3.14015

1.64490

1.91

0.0666

-0.22927

6.50957

Generated by the SAS System (Local, XP_PRO) on 01JUL2010 at 8:43 AM

X1

X2

Y

predicted_Y

lclm_Y

uclm_Y

lcl_Y

ucl_Y

residual_Y

27

13

124

116.0419044

101.3022

130.7816

63.74829

168.3355

7.958095614

82

11

198

204.480575

186.9

222.0612

151.3163

257.6448

-6.48057497

11

7

75

69.64637309

51.49078

87.80197

16.2892

123.0035

5.353626911

56

12

182

162.8444845

149.6269

176.0621

110.9593

214.7296

19.15551549

15

12

80

92.23579244

77.55883

106.9128

39.95984

144.5117

-12.2357924

32

10

125

115.2322606

105.3849

125.0796

64.10171

166.3628

9.767739386

15

7

74

76.53502597

59.36529

93.70476

23.5052

129.5648

-2.53502597

37

9

129

120.7029234

111.0457

130.3601

69.60866

171.7972

8.297076572

27

7

165

97.20098463

82.56136

111.8406

44.9355

149.4665

67.79901537

13

9

46

79.37100612

64.87381

93.8682

27.14523

131.5968

-33.3710061

50

9

153

143.0910453

133.6014

152.5807

92.02819

194.1539

9.908954696

37

15

137

139.5438432

119.7008

159.3869

85.58915

193.4985

-2.54384318

68

7

162

167.8096767

153.2863

182.3331

115.5766

220.0427

-5.8096767

17

11

104

92.53996559

79.3753

105.7046

40.66829

144.4116

11.46003441

56

6

140

144.0035648

128.6644

159.3427

91.53785

196.4693

-4.00356475

37

8

114

117.5627701

106.488

128.6376

66.18171

168.9438

-3.56277014

53

6

192

138.8370751

123.6206

154.0536

86.40708

191.2671

53.16292491

17

13

115

98.82027217

82.79669

114.8439

46.15038

151.4902

16.17972783

26

10

133

104.8992813

94.05075

115.7478

53.56651

156.2321

28.10071871

70

14

213

193.2350762

172.4939

213.9762

138.9437

247.5265

19.76492381

82

8

175

195.0601151

178.546

211.5742

142.2389

247.8813

-20.0601151

62

11

188

170.0373105

157.5947

182.4799

118.3442

221.7304

17.96268945

84

10

204

204.7847481

187.6284

221.9411

151.7593

257.8102

-0.78474812

43

6

85

121.6154429

106.276

136.9549

69.14965

174.0812

-36.6154429

59

9

148

158.5905143

147.9802

169.2008

107.3076

209.8735

-10.5905143

8

14

55

86.46095647

66.82185

106.1001

32.58093

140.341

-31.4609565

75

8

155

183.0049725

168.3037

197.7062

130.7222

235.2878

-28.0049725

8

6

29

61.33973013

40.23783

82.44163

6.909476

115.77

-32.3397301

79

9

179

193.0337787

177.7

208.3676

140.5696

245.4979

-14.0337787

11

15

75

94.76759943

73.28023

116.255

40.18675

149.3485

-19.7675994

87

8

193

203.6709312

185.7646

221.5772

150.3981

256.9438

-10.6709312

Quiz 9

A dealer of matchbox cars believes that the price received for the cars at an auction increases with the age (X1) of the cars and with the number of people bidding (X2) on the car. Data was collected at a big national show and auction in Chicago Illinois and is presented on blackboard.

Now using SAS only answer the following: The instructions are on page 2.

1. Write down the regression model.                           

2. Write down the prediction equation.

3. Predict y when the age is 11 years and the # of bidders is 15. What is the residual?

4. SSE =

S2 =

S =

  R2 =        now interpret R2.

5. Write down 95% confidence intervals for b1 and b2.

6. Test if the age of the car is a significant variable.

7. Test if the number of bidders is a significant variable.

8. Find the 95% confidence interval for E(Y) when the age is 11 years and the # of bidders is 15.

9. Find the 95% prediction interval for Y when the age is 11 years and the # of bidders is 15.

1. Click on start -- go to programs -- go to SAS -- go to Enterprise Guide 4.0

          a. a. If you get the welcome window then x it out.

          b. Go up to file and down to import data (after downloading from black board )

           c.   click on local computer

          d. click on the correct data file(it will be an excel file) then click open

           e.   click the first file name in the next window and then click open

           d. then click run in the next window

          f. when the data appears then you are ready to proceed

2. Go up to the menu on the top row and click Analyze and drag down to Regression and over to Linear. Click yes to continue

4. Click on X1, and X2(if using the shift key you can declare them all at once) then click on the right arrow and then click on explanatory variables

          a. Click on Y then click on the right arrow and then click on dependent variables

5. Click on statistics then click on confidence limits for parameter estimates and leave at 95%

6. Click on predictions and then click on original sample and residual and prediction limits.

7. Click on titles then click on Use default text (to uncheck it and write your own).   Then click in the big box and type the name of the worksheet and your name or names.

8. Then click run (this "submits" or "runs” the program).

9. Then you will see an analysis window. Then print this page using the print command.

10. Then on the left side under Project Explorer, double click on Linear regression predictions and statistics for (the file name you give it). If you have blank columns you may delete them after going up to data and dragging down to read only. There are two columns you will not need. Thus you can delete the last 2 columns. Then print this table.

11. An optional way to print is go up to file and drag down to send to and over to either excel or word. Then print from that file.

Linear Regression Results quiz 9

Explanation / Answer

1)Model:Linear Regression Model

2)y=28.7215+1.72216*(age of car)+3.14015*(# bidders)

3)Check in the data for X1=11,and X2=15 gave a y=75 and predicted=94.7676 and a residual=-19.7676

4)ss=76551,sse=14799 ,R^2=0.7806

5)95% CI

b1= [1.36863,2.07569]

b2=[-0.22927,6.50957]

6)P value of age of car<0.001 Hence it is a significant

7)P value for bidder is 6% which is not significant at 10% level.Hence #bidders is not a significant value

8)95% CI for E[Y]= [73.28023,116.255]

9)95% CI for Y=[40.18675,149.3485]

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