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;

            Н_a: r²0.

 Select the level of criticality Prob_крит.=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

Prob_факт. (F)=0,011 is less than Prob_крит. =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