Question
YearRate_(%)
198710.5
198810.54
19899.65
19909.59
19918.13
19927.8
19936.83
19947.35
19956.88
19967.18
19976.67
19986.5
19996.8
20007.09
20016.03
20025.92
20035.91
20045.69
20055.96
20065.84
20075.72
20084.91
20094.72
20104.55

k=1k=1k=2k=2k=3k=3
nd Ld Ud Ld Ud Ld U
151.081.360.951.540.821.75
161.11.370.981.540.861.73
171.131.381.021.540.91.71
181.161.391.051.530.931.69
191.181.41.081.530.971.68
201.21.411.11.5411.68
211.221.421.131.541.031.67
221.241.431.151.541.051.66
231.261.441.171.541.081.66
241.271.451.191.551.11.66
251.291.451.211.551.121.66

  1. The forecasted average December mortgage rate in 2011 is __% (Round to two decimal places as needed.)

  2. Calculate the MAD for this forecast. (Round to two decimal places as needed.)

  3. Determine the Durbin-Watson statistic (Round to two decimal places as needed.)

  4. Identify the critical values. (Round to two decimal places as needed.)

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

Excel ADDon Megastat used.

A.

The forecasted average December mortgage rate in 2011 is __% ​(Round to two decimal places as​ needed.)

Regression Analysis

r²

0.860

n

24

r

-0.928

k

1

Std. Error of Estimate

0.645

Dep. Var.

Rate(%)

Regression output

confidence interval

variables

coefficients

std. error

   t (df=22)

p-value

95% lower

95% upper

Intercept

a =

9.718

0.272

35.740

5.56E-21

9.154

10.282

t

b =

-0.222

0.019

-11.643

7.08E-11

-0.261

-0.182

ANOVA table

Source

SS

df

MS

F

p-value

Regression

56.455

1  

56.455

135.57

7.08E-11

Residual

9.162

22  

0.416

Total

65.616

23  

The fitted model is Yt = 9.718 - 0.2216×t

When t=25( year =2011). Predicted Rate =9.718 - 0.2216*25 =4.178

= 4.18 ( two decimals)

B.

Calculate the MAD for this forecast. ​(Round to two decimal places as​ needed.)

t

Rate(%)

Predicted

Absolute Residual

1

10.500

9.496

1.004

2

10.540

9.275

1.265

3

9.650

9.053

0.597

4

9.590

8.832

0.758

5

8.130

8.610

0.480

6

7.800

8.389

0.589

7

6.830

8.167

1.337

8

7.350

7.945

0.595

9

6.880

7.724

0.844

10

7.180

7.502

0.322

11

6.670

7.281

0.611

12

6.500

7.059

0.559

13

6.800

6.838

0.038

14

7.090

6.616

0.474

15

6.030

6.394

0.364

16

5.920

6.173

0.253

17

5.910

5.951

0.041

18

5.690

5.730

0.040

19

5.960

5.508

0.452

20

5.840

5.287

0.553

21

5.720

5.065

0.655

22

4.910

4.843

0.067

23

4.720

4.622

0.098

24

4.550

4.400

0.150

MAD

0.506

MAD= 0.51 ( two decimals)

C.

Determine the​ Durbin-Watson statistic ​(Round to two decimal places as​ needed.)

Durbin-Watson statistic= 0.60

D.

Identify the critical values. ​(Round to two decimal places as​ needed.)

Critical values for n=24 and K=1 is ( 1.24, 1.45).

Obtained Durbin-Watson statistic value = 0.60 which is less than the lower limit dL 1.24.

This suggests there is presence of positive auto correlation.

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