# 3 tasks of econometrics (MESI)

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# Description

According to engineering companies, methods of correlation analysis to explore the relationship between the following parameters: X1- margin (%); X2 - bonuses and compensation per employee (mln. Rub.); X3-capital productivity
Table 1.
N p / p X1 X2 X3
1 13.26 1.23 1.45
2 10.16 1.04 1.3
3 12.82 0.43 1.65
4 10.63 0.88 1.91
5 9.12 0.57 1.68
6 25.83 1.72 1.94
7 23.39 1.89 1.7
8 14.68 0.84 1.94
9 10.05 2.06 0.6
1. Of the proposed data cross off the line with the number corresponding to the last digit of the record book.
2. Calculate the mean vector and standard deviations, correlation coefficients matrix pair
3. Calculate the partial correlation coefficient r12 / 3 and r13 / 2.
4. calculate the correlation matrix R evaluation of multiple correlation coefficient r1 / 23
5. If a = 0,05 check the significance of all the paired correlation coefficients.
6. If a = 0,05 check importance partial correlation coefficient r12 / 3 and r13 / 2
7. If a = 0,05 check multiple significance of the correlation coefficient.

According to the agricultural areas of the region requires to build a regression model of productivity based on the following indicators:
Y- cereal yields (t / ha);
X1 - the number of wheel tractors per 100 hectares;
X2 - the number of combine harvesters per 100 hectares;
X3 - number of guns on the soil surface treatment of 100 hectares;
X4 - the amount of fertilizer being spent per hectare (t / ha);
X5 - the number of plant protection chemicals, consumables per hectare (kg / ha)

Table 4.
Y X1 X2 X3 X4 X5
1 9.7 1.59 0.26 2.05 0.32 0.14
2 8.4 0.34 0.28 0.46 0.59 0.66
3 9.9 4.63 0.4 6.44 0.43 0.59
4 9.6 2.16 0.26 2.16 0.39 0.16
5 8.6 0.3 2.16 2.69 0.37 0.17
6 12.5 0.68 0.29 0.73 0.42 0.23
7 7.6 0.35 0.26 0.42 0.21 0.8
8 0.52 0.24 0.49 6.9 0.2 0.8
9 13.5 3.42 0.31 3.02 1.37 0.73
10 9.7 0.3 1.78 3.19 0.73 0.17
11 10.7 2.4 3.3 0.32 0.25 0.14
12 12.1 9.36 0.4 0.39 11.51 0.38
13 9.7 1.72 0.28 2.26 0.82 0.17
July 14 0.59 0.29 0.6 0.13 0.35
15 7.2 0.28 0.26 0.3 0.09 0.15
16 8.2 1.64 0.29 1.44 0.2 0.08
17 8.4 0.09 0.22 0.05 0.43 0.2
18 13.1 0.08 0.25 0.03 0.73 0.2
19 8.7 1.36 0.26 0.17 0.99 0.42
1. Of the proposed data cross off the line with the number corresponding to the last digit of the record book.
2. The correlation analysis: analyze the relationship between the variable and the resultant factor variables on the correlation matrix, identify multicollinearity.
3. Build the regression equation with the significant coefficients using stepwise regression analysis algorithm.
4. Choose the best of the resulting regression models based on the analysis of the coefficient of determination, residual variance arising from the interpretation of economic models.

Activity 3
According to the data presented in Table., To classify n = 5 of engineering, data on the activities which are characterized by parameters: x (1) -Cost-effective (%), x (2) - labor productivity (mln. Rub. / Pers.)
Number
Company 1 2 3 4 May
xi (1) 7 4 5 3 6
xi (2) 5 9 4 April 7
For the distance between the object to take a weighted Euclidean distance w1 = 0,9 and w2 = 0,1, and the distance between the clusters measured on the basis of:
a) the "nearest neighbor";
b) "long-neighbor";
c) to compare the division into two clusters on the criterion of minimum sum of intraclass variance.

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