Modeling a pairwise linear regression in Eviews(video lesson)

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Modeling a pairwise linear regression in Eviews.

       Based on sample data for the population of agricultural organizations on the value of gross agricultural output per 100 ha of agricultural land (thousand rubles), let us denote the variable y, and the value of fixed assets per 100 ha of agricultural land (thousand rubles) - x squared, is required:

1.    to model a pairwise linear regression: ;

2.     to assess the reliability of the equation in general, using the method of variance analysis;

3.     to assess the closeness of the link in the regression equation on the basis of the coefficient of determination;

4.     to assess the reliability of the individual parameters of the equation;

5.     to give an interpretation of the full regression coefficient;

6.     to plot the regression equation on a scatter plot.

Working procedure

1. To make a regression equation in Eviews, select "Quick" - "Estimate Equation" in the main menu, select the variables: first the dependent, then the independent and then enter the constant "c":

 

Another method. First select the dependent variable (y) and then, holding "Ctrl", the independent variable (x2), right-click, select "Open", "as Equation":

 

 

 

The variables will be entered automatically. The default method of parameter estimation is LS (Least Squares), and we end up with regression results. (figure 4.1)

A regression equation is obtained: , (y equals four thousand one hundred and six point one one four plus zero point one four zero nine  multiplied by x squared) determination coefficient (r2)– R square – is 0,161.                                  Since the regression equation is based on sample data, an assessment of its validity is necessary. The Eviews results display the actual value of Fisher's F-criterion and its actual significance (probability), allowing for a variance analysis.

 

 

 

 

 

 

 

 

Dependent Variable: Y

 

 

Method: Least Squares

 

 

Date: 11/24/21   Time: 16:00

 

 

Sample: 1 39

 

 

 

Included observations: 39

 

 

 

 

 

 

 

 

 

 

 

 

Variable

Coefficient

Std. Error

t-Statistic

Prob.  

 

 

 

 

 

 

 

 

 

 

X2

0.140901

0.052828

2.667151

0.0113

C

4106.114

424.2004

9.679656

0.0000

 

 

 

 

 

 

 

 

 

 

R-squared

0.161258

    Mean dependent var

5075.147

Adjusted R-squared

0.138590

    S.D. dependent var

1473.304

S.E. of regression

1367.406

    Akaike info criterion

17.32914

Sum squared resid

69182549

    Schwarz criterion

17.41445

Log likelihood

-335.9182

    Hannan-Quinn criter.

17.35975

F-statistic

7.113695

    Durbin-Watson stat

1.868320

Prob(F-statistic)

0.011281

 

 

 

 

 

 

 

 

 

 

 

 

 


Figure 4.1 - The results of pairwise linear regression in Eviews.

2. Let us introduce the working hypothesis that the coefficient of determination is equal to zero, and the alternative hypothesis that the coefficient of determination is not equal to zero: Н0: r2=0;

            Нa: r20.

 Select the level of criticality Probкрит.=0,05

It should be remembered that if the actual significance of the criterion is less than the critical significance, then the alternative hypothesis is accepted.

In our case, a valid regression equation is obtained, since

Probфакт. (F)=0,011 is less than Probкрит. =0,05 (the actual value is zero zero eleven is less than the critical value of zero zero five).

3. The coefficient of determination is not zero.

The coefficient of determination is one of the most important indicators of the closeness of the link and the quality of the regression model.

In our model the coefficient of determination is equal to 0.16, that is to say 16% of the variation in the gross yield is explained by the variation in the cost of fixed assets.

4. Let us estimate the reliability of the parameters of the regression equation using the t-test.

Let us introduce the null hypothesis (parameters of the general regression equation are not reliable) and the alternative hypothesis (parameters are reliable):

;;

Statistical inference is made by comparing the actual and critical significance of the Student's t-test criteria:

The significance of the constant is less than 0.05, hence with a 95% confidence level the hypothesis that the constant in the general regression equation is valid should be accepted.

Significance of the slope coefficient is 0.011, which is less than 0.05. Consequently, with the level of confidence of 95%, we accept the hypothesis of reliability of the slope coefficient in the general regression equation.

5. The resulting regression slope coefficient shows that if the costs of fixed assets increase by 1 thousand rubles, the value of gross yield will increase by 0.14 thousand rubles.

6. Let us draw a scatter plot and add a regression line to it by first selecting the independent variable (x2) and then the dependent variable (y), selecting "Quick" and "Graph" in the main menu, and in the window that appears:

 Select the graph type "Scatter", which means "scatter", and add a regression line in the "Fit lines" - "Regression line" field, resulting in a graph (figure 4.2).

Figure 4.2 - Scatter plot of y as a function of x2 and regression line.

It is required to calculate the forecast values, give their point and interval estimation, and plot the forecast graph.

          In order to calculate the forecast values, we need to open the regression results and select "Forecast" in it, in the opened window denote the forecast values yf, and the average forecast error se. We will get the forecast plot shown in Figure 1.

Figure 1 - Forecast, lower and upper limit of the forecast.

In automatic mode, the forecast values (yf) and the average error of the individual forecast (se) have been calculated, and the upper and lower limits are not automatically determined, so we will perform their calculations. To do this, we need to determine the critical t-Student value using the formula:

scalar tc=@qtdist(.975,37), we end up with tc = 2,026192. The number of degrees of freedom is defined as n-2 for pairwise regression: 39-2=37.

Calculate the lower limit of the forecast: series yf_lb=yf-tc*se, the upper limit:

 series yf_ub=yf+tc*se. The results of the calculations are presented in Table 1.

          Table 1 - Accuracy assessment indicators for individual forecasting.

 

 

Y

YF

SE

YF_LB

YF_UB

1

2326.992749518304

4234.078776406739

1420.275855831241

1356.32654189926

7111.831010914219

2

3280.243902439024

4371.248808244754

1409.749146820262

1514.825712195821

7227.671904293687

3

4262.942926697322

4471.984595949711

1403.169130388682

1628.893879601052

7315.07531229837

4

4486.553220713074

4499.716449348929

1401.530953191444

1659.944995290421

7339.487903407436

5

3106.108202443281

4502.358758590847

1401.378792054854

1662.895612280464

7341.82190490123

6

4175.319767441861

4511.778485017906

1400.841910146723

1673.403164783313

7350.153805252499

7

6094.82801367968

4632.178548974107

1394.749333372211

1806.147961880458

7458.209136067756

8

3631.190275615764

4642.277973412172

1394.303504781585

1817.150720848651

7467.405225975694

9

5320.73708519509

4643.197195550337

1394.263430195521

1818.151141811057

7468.243249289616

10

5898.267258203659

4706.722639674003

1391.697941127422

1886.874760548491

7526.570518799515

11

2307.775631578947

4712.916399896925

1391.469364471333

1893.531661069204

7532.301138724646

12

4958.902946542214

4741.472882404329

1390.465183392691

1924.12280770967

7558.822957098989

13

7920.680125879919

4753.052085357441

1390.08129600599

1936.479840392367

7569.624330322515

14

4791.462545454545

4755.769266253945

1389.993161759979

1939.375598233873

7572.162934274017

15

6945.315161839864

4763.741244923467

1389.738860838084

1947.862839514681

7579.619650332254

16

4612.459574468086

4764.812419701954

1389.705177442753

1949.002263334915

7580.622576068994

17

3799.371292392301

4783.24079546537

1389.143746052214

1968.56820715035

7597.913383780389

18

3233.470507544582

4798.965535473048

1388.691685399298

1985.208909045799

7612.722161900296

19

5125.122189638319

4815.592512519083

1388.240761620635

2002.74954445356

7628.435480584608

20

3805.444444444444

4818.385563074447

1388.167746080948

2005.690538545123

7631.080587603773

21

4084.060953230187

4826.268085678166

1387.965922960246

2013.981993634872

7638.554177721459

22

5905.781451861602

4919.152497763576

1386.06021743731

2110.727731887608

7727.577263639544

23

5843.90243902439

5080.853012170129

1384.827335114368

2274.926303164709

7886.77972117555

24

6870.840828757048

5108.057164951543

1384.880653921335

2302.022421781309

7914.091908121778

25

4785.758934317917

5108.66795290372

1384.882713256843

2302.629037123401

7914.706868684039

26

6679.16260725938

5129.410509078749

1384.975125490163

2323.184348327783

7935.636669829714

27

4735.791228906249

5147.682690115186

1385.092702609005

2341.2182954922

7954.147084738172

28

3370.177073625349

5205.708661763007

1385.690604384924

2398.03280306802

8013.384520457993

29

5730.788447069944

5433.482704229655

1391.32760842541

2614.385190433771

8252.580218025538

30

7926.314136666666

5441.764274225697

1391.630872385633

2622.052289279302

8261.476259172093

31

4564.028283870968

5551.533970813713

1396.296775339051

2722.367968469876

8380.699973157549

32

7024.566336123151

5608.491118555878

1399.188797667514

2773.465322367199

8443.516914744556

33

8218.414553979024

5734.058495290689

1406.689161401848

2883.835518633524

8584.281471947852

34

5558.597669648227

5772.327914427941

1409.279867615615

2916.855668366521

8627.800160489361

35

4781.242733333334

5786.291463108864

1410.260317499896

2928.832636881536

8643.750289336193

36

4699.342105263158

5895.844704343945

1418.599676415368

3021.488731935592

8770.200676752298

37

5137.387606212424

5960.039015662769

1424.01417321137

3074.712230655261

8845.365800670275

38

6312.665708887833

6205.873132807589

1448.265113658511

3271.409275044715

9140.336990570463

39

5618.713087328767

7091.725702965597

1577.782851959087

3894.83398002952

10288.61742590167



       In farm No.1 the forecast value is 4234, and the actual value is 2327 that is there is a reserve of growth of gross harvest by 1907 thousand rubles. Let us give a point estimation of the forecast: forecast value for farm 1 will be 4234 thousand rubles with average error of 1420 thousand rubles. Interval estimation of the forecast: with 95% confidence level the forecast will fall in the confidence interval from 1356 to 7112 thousand rubles.

Video tutorial on solving this problem in Eviews

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