Final Model Summary Table Intercept TemperatureW Winter Rain Harvest Rain Vintag

Question

Final Model Summary Table Intercept TemperatureW Winter Rain Harvest Rain Vintage Standard Error Coefficient P-value Prediction Table Winter RainHarvest Rain Vintage Price 95% PI-Lower Limit Est Price 95% PI-Upper Limit Temperature 17.12 16.73 17.15 16.13 16.42 690 502 420 582 485 763 830 697 608 402 602 819 714 610 575 622 551 536 18.87 15.62 12.47 11.97 19.31 11.49 27.18 13.92 11.83 13.58 11.12 16.05 12.11 130 110 187 187 290 16.42 17.33 16.3 15.72 17.27 15.37 16.53 16.23 155 267 118 292 244 16.55 16.67 16.77 14.98 17.07 16.30 16.95 17.65 15.58 15.82 16.17 16.00 112 158 123 184 11.24 14.98 13.13 11.06 11.69 574 572 418 821 763 13.51 12.88 11.13 13.10 12.39 11.46 247 6 122 4 578

Explanation / Answer

Using MS Excel to perform the analysis:

Data > data analysis > regression

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.812243595

R Square

0.659739658

Adjusted R Square

0.597874141

Standard Error

2.219012319

Observations

27

ANOVA

Df

SS

MS

F

Significance F

Regression

4

210.0406552

52.51016

10.66409

5.84459E-05

Residual

22

108.3283448

4.924016

Total

26

318.369

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Lower 95.0%

Upper 95.0%

Intercept

-42.482066

13.07483997

-3.24915

0.00368

-69.597625

-15.366508

-69.597625

-15.366508

temp

3.040574031

0.737074739

4.125191

0.000444

1.511974588

4.569173473

1.511974588

4.569173473

winter rain

0.010263593

0.003734263

2.748493

0.011726

0.002519207

0.01800798

0.002519207

0.01800798

harvest rain

-0.0150810

0.006253748

-2.41152

0.024677

-0.0280504

-0.0021115

-0.0280504

-0.00211152

vintage

0.120802538

0.055497162

2.176734

0.040513

0.005708468

0.235896607

0.005708468

0.235896607

95% Confidence interval for y = y ± t/2 * s.e(y)

Where y is the predicted value

t/2 is the t table value for =0.05 for n-2 df

s.e(y) is the standard error of y (from the output, s.e(y)= 2.219012319

t/2 = 1.708 (from t table) for 25 df

obs 1: 17.06263384 ± 1.708*2.219012319

lower limit = 17.06263384 - 1.708*2.219012319 = 13.2725608

upper limit =17.06263384 + 1.708*2.219012319 =20.85271

Observation

Predicted price

lower pl

upper pl

1

17.06263384

13.2725608

20.85271

2

17.88621156

14.09613852

21.67628

3

16.23804159

12.44796855

20.02811

4

12.35505654

8.564983499

16.14513

5

13.61748486

9.82741182

17.40756

6

15.72412225

11.93404921

19.5142

7

13.68024621

9.890173165

17.47032

8

20.81444111

17.02436807

24.60451

9

15.9856553

12.19558225

19.77573

10

11.63451607

7.84444303

15.42459

11

15.00208262

11.21200958

18.79216

12

8.578055489

4.787982448

12.36813

13

16.94118123

13.15110819

20.73125

14

14.3479369

10.55786386

18.13801

15

10.44440784

6.654334795

14.23448

16

11.75246889

7.962395849

15.54254

17

14.81648055

11.02640751

18.60655

18

13.92415708

10.13408404

17.71423

19

7.513046708

3.722973667

11.30312

20

12.6327043

8.842631262

16.42278

21

11.28290966

7.492836614

15.07298

22

13.31400617

9.52393313

17.10408

23

12.5948554

8.804782355

16.38493

24

12.72925416

8.939181122

16.51933

25

13.28581732

9.495744278

17.07589

26

12.68633875

8.896265706

16.47641

27

11.34588761

7.555814569

15.13596

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.812243595

R Square

0.659739658

Adjusted R Square

0.597874141

Standard Error

2.219012319

Observations

27

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