# Modeling a pairwise linear regression in Eviews(video lesson)

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A video tutorial on solving this problem is at the bottom of the page.

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: r2 0.

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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