Modeling a pairwise linear regression in Eviews(video lesson)
Below is the condition of the problem and the text part of the solution. The download of the complete solution, doc and wf1 files in the rar archive, will start automatically in 10 seconds.
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: 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.
Имя файла: linear-regression.rar
Размер файла: 373.84 Kb
Если закачивание файла не начнется через 10 сек, кликните по этой ссылке