CC BY
6
Abdurakhmanova Z. doctoral student TSUE
INDICATOR OF FOOD PRODUCTION IN UZBEKISTAN AND
FACTORS AFFECTING IT
Abstract: In the article, we studied the factors influencing the food production index. Factors include agricultural land, per capita expenditure, import volume index, rural population, export volume index and cereal crop yield. These variables are denoted by y and x1, x2, x3, x4, x5, x6 respectively. In addition, the relationship between the residuals was checked using the Heteroscedasticity test and found to be normally distributed. Data for variables were obtained from https://databank.worldbank.org/source/world-development-indicators?l=en.
The relationship between these variables was checked with multicollinearity, and we also checked how reliable the data of the variables was using the STATA 17program.
Keywords: OLS, regression, correlation, model parameters, model estimation, export volume index, import volume index, agroculture.
Methods and Materials. Building mathematical models based on statistical data representing economic and social processes and using these models to make predictions, we will consider the relevant conclusions on the example of the following problem.
Literature review. Based on a systematic literature review, it takes stock of existing social sustainability indicators, analyses their structure and evolution, and proposes critical considerations for selecting indicators relevant to the current period. Three sub-questions guide this research. First, what indicators exist on the social dimension of sustainability, and how are they defined? Second, how can these indicators be structured according to conceptually and empirically relevant themes? And third, how has the meaning of the main indicators evolved over time? While our first question is straightforward, structuring social indicators (second question) by theme, although seemingly more intuitive, can be risky due to the lack of conceptual clarity when deriving them [1]
Circular resource use in agriculture and food systems could play an important role when aiming for sufficient food output with limited environmental impact and resource depletion. Circularity, however, is not a goal in itself. With respect to nutrient use and emissions, agricultural system sustainability is currently commonly assessed by nutrient output/input ratio (O/I, nutrient use efficiency) or surplus per ha (I-O) [2]
The food security indicators can primarily be grouped into four dimensions represented by the availability of food, access to food, potential utilization and
stability of food production. Each of the identified indicators that are independent of each other can be utilised to assign individual values based upon actual statistics and observations available for each country. The projection of these statistical values for evaluating future food security can also be done once the appropriate methodology is available for making projections [3]
Introduction. Food production index is an index that includes all phases of production and consumption related to the food sector in a country or region. Factors influencing this index are:
-Activities in the field of agriculture: Proper and efficient activities in the field of agriculture are of great importance in obtaining food production index. Energy prices: Energy prices affect the index because they increase the amount of energy needed to produce food.
-Transport services: Food transport is one of the important factors affecting food production index. The cost and quality of transportation services can increase or decrease the index of food production.
-Political and economic situation: Political and economic situation is one of the important factors affecting food production index. If the economic situation is good, the food production index will also increase.
-Joint trade: Joint trade is one of the factors affecting food production index. Food export-import can increase or decrease the index.
-Fiscal Policy: Fiscal policy is one of the important factors affecting food production index. If the fiscal policy is good, the index will also increase.
-Demography: Demography is one of the factors influencing food production index. Changes in the number and composition of the population can increase or decrease the index.
- Technological development: Technological development is one of the important factors influencing food production index. If the technological development is good, the index will also increase.
-Tourism activity: Tourism activity is one of the factors affecting food production index. The development of activities in the field of tourism can increase or decrease the index.
In the article, we want to study and analyze other factors affecting food production index. Factors include agricultural land, per capita expenditure, import volume index, rural population, export volume index and cereal crop yield. The data was taken from the World Bank, which studied the data of Uzbekistan for the period from 2003 to 2020. There y=food production index, x1=Agricultural land (%), x2=Expenditure per capita $, x3=Import volume index (2000 = 100), x4=% of rural population, x5=Export volume index, x5=Grain yield (kg per hectare)
Yil Y x1 x2 x3 x4 x5 x6
2003 43.59 61.6343601520 15.0751471 93.7985686 52.429 100.292814 3522.4
2004 45.52 61.2224763853 16.5599636 111.327931 51.946 120.379680 3596.1
2005 48.66 60.807756814 18.5837609 114.754813 51.463 118.625261 4042.1
2005 54.3 60.3923368131 21.4218209 131.453918 50.979 111.616691 4103.2
2007 56.05 59.9586223347 27.0282577 178.061288 50.495 145.682170 4396.9
2008 59.08 59.5457913098 34.8361878 238.191658 50.011 150.805094 4285.3
2009 64.11 59.1336063035 40.2692118 234.509710 49.528 182.330261 4553.1
2010 68.9 58.7255558716 53.4781476 219.062830 49.044 157.47343 4434.2
2011 73.94 58.3214206223 63.4045761 241.339903 48.85 139.706935 4414.5
2012 80.17 57.9072969251 71.3737475 279.714610 48.95 129.804959 4597.9
2013 86.92 57.5048934231 78.2416559 313.476190 49.05 144.558919 4746.4
2014 93.08 58.6109332727 53.3899822 335.917682 49.15 144.629185 4806.6
2015 100.51 57.9845665002 63.7842766 299.885148 49.25 136.086054 4835.2
2016 106.41 57.9805306962 70.5774287 303.151333 49.35 134.975874 4827.0
2017 101.18 57.9525543137 52.7453972 310.674899 49.45 138.986859 4298.2
2018 105.11 57.9234067278 49.6840134 426.216918 49.522 134.275291 4102.4
2019 105.23 58.0070592775 56.8701192 545.302953 49.567 180.799234 4533.6
2020 106.96 58.2832179734 64.0036967 498.465745 49.584 166.677777 4481.1
Descriptive Statistics
Variable Obs Mean Std. Dev. Min Max
Yil 18 2011.5 5.339 2003 2020
Y 18 77.762 23.352 43.59 106.96
x1 18 58.994 1.289 57.505 61.634
x2 18 47.296 20.558 15.075 78.242
x3 18 270.85 127.421 93.799 545.303
x4 18 49.923 1.084 48.85 52.429
x5 18 140.984 21.76 100.293 182.33
x6 18 4365.344 381.063 3522.4 4835.2
This table shows the descriptive statistics for seven variables, including the number of observations (Obs), mean, standard deviation (Std. Dev.), minimum value (Min), and maximum value (Max). The variable "yil" represents the year and has 18 observations with a mean of 2011.5 and a standard deviation of 5.339. The minimum value is 2003, and the maximum value is 2020. The variable "y" represents some numerical value and has 18 observations with a mean of 77.762 and a standard deviation of 23.352.
The minimum value is 43.59, and the maximum value is 106.96. The variables x1, x4, x5, and x6 are all numerical values with 18 observations each. x1 has a mean of 58.994 and a standard deviation of 1.289, with a minimum value of 57.505 and a maximum value of 61.634. x4 has a mean of49.923 and a standard
deviation of 1.084, with a minimum value of 48.85 and a maximum value of 52.429. x5 has a mean of 140.984 and a standard deviation of 21.76, with a minimum value of 100.293 and a maximum value of 182.33. x6 has a mean of 4365.344 and a standard deviation of 381.063, with a minimum value of 3522.4 and a maximum value of 4835.2. The variables x2 and x3 are also numerical values with 18 observations each. x2 has a mean of 47.296 and a standard deviation of 20.558, with a minimum value of 15.075 and a maximum value of 78.242. x3 has a mean of 270.85 and a standard deviation of 127.421, with a minimum value of 93.799 and a maximum value of 545.303.
Figure 1 There is a negative relationship between the dependent variables x1 and x4 and y, and this relationship is well correlated. There is a positive correlation between the variables x2 and x3 and y, and there is a good correlation. There is a positive but less significant correlation between variables x5 and x6 and y.
• J • •
49
50
51 x4
52
53
s ° -oo
3500
4000 4500
x6
5000
Figure 3 above shows the relationship between x1,x2,x3,x4,x5,x6 and y. It is known from the regression line that these variables are normally distributed.
n-1-1-1-r
0.00 0.25 0.50 0.75 1.00
Empirical P[I] = I/(N+1)
• Y - Fitted values
Pairwise correlations
Variables (1) (2) (3) (4) (5) (6) (7)
(1) y 1.000
(2) x1 - 1.000
0.882
(0.00
0)
(3) x2 0.810 - 1.000
0.946
(0.00 (0.00
0) 0)
(4) x3 0.891 - 0.688 1.000
0.781
(0.00 (0.00 (0.00
0) 0) 2)
(5) x4 - 0.939 - - 1.000
0.727 0.895 0.642
(0.00 (0.00 (0.00 (0.00
1) 0) 0) 4)
(6) x5 0.439 - 0.440 0.649 - 1.000
0.534 0.605
(0.06 (0.02 (0.06 (0.00 (0.00
8) 2) 8) 4) 8)
(7) x6 0.665 - 0.813 0.547 - 0.569 1.000
0.809 0.863
(0.00 (0.00 (0.00 (0.01 (0.00 (0.01
3) 0) 0) 9) 0) 4)
This scatterplot shows the relationship between social studies scores and reading scores for a group of students. The dots represent individual students, with their social studies score on the x-axis and their reading score on the y-axis. The line of best fit (lfit) is also shown, which represents the trend in the data. The pairwise correlations table below the plot shows the strength and direction of the correlation between each variable. For example, there is a strong negative correlation (-0.882) between social studies scores (x1) and reading scores (y), meaning that as social studies scores increase, reading scores tend to decrease. Conversely, there is a strong positive correlation (0.810) between social studies scores (x1) and another variable, x2. Overall, this scatterplot and correlation table provide a visual and numerical summary of the relationship between social studies and reading scores in this group of students.
Spearman's rank correlation coefficients
Variables (1) (2) (3) (4) (5) (6) (7)
(1) y 1.000
(2) x1 -0.810 1.000
(3) x2 0.765 -0.856 1.000
(4) x3 0.936 -0.800 0.711 1.000
(5) x4 -0.523 0.738 -0.810 -0.501 1.000
(6) x5 0.414 -0.207 0.354 0.478 -0.300 1.000
(7) x6 0.631 -0.628 0.825 0.577 -0.701 0.459 1.000
Spearman rho = 0.459
The Spearman's rank correlation coefficient for the relationship between social studies scores and reading scores is 0.459. This indicates a moderate positive correlation between the two variables, meaning that as social studies scores increase, reading scores tend to increase as well, but not strongly. It is important to note that this correlation coefficient is different from the Pearson correlation coefficient mentioned in the previous paragraph, as Spearman's rank correlation coefficient measures the strength and direction of the relationship between two variables based on their ranks rather than their actual values.
Figure2 The graph show s that the given variables are not normally distributed. According to the box plot, 75% of the data is between 50 and 100.
o
o -
40 60 80 Y 100 Linear 120 o
regression
Y Coef. St.Err. t- value P-value [95% Conf Interval] Sig
x1 -15.652 7. - 1.
889 1.98 073 33.015 711
x2 -.202 .2 - .4
82 0.72 488 .823 19
x3 .112 .0 .0 .1
34 .30 007 37 86 **
x4 8.084 7. - 23
145 .13 282 7.642 .81
x5 -.269 .1 - .0
46 1.85 092 .59 52
x6 .015 .0 - .0
1 .57 146 .006 36
Constant 549.702 32 - 12
8.479 .67 122 173.275 72.679
Mean dependent var 77.762 SD dependent 23.352
var
R-squared 0.940 obs Number of 18
F-test 28.660 Prob > F 0.000
Akaike crit. (AIC) 126.873 Bayesian crit. 133.105
(BIC)
*** p<.01, **p<.05, *p<.1
This is the output of a linear regression model with y as the dependent variable and x1, x2, x3, x4, x5, and x6 as the independent variables. The table shows the coefficients, standard errors, t-values, p-values, and confidence intervals for each independent variable, as well as the constant term. The mean and standard deviation of the dependent variable, R-squared value, number of observations, F-test statistic, and AIC and BIC values are also provided. The significance levels for each coefficient are indicated by asterisks (*, **, or ***) based on their p-values._
Test scale = mean(unstandardized items) Reversed items: x1 x4 Average interitem covariance:2462.005 Number of items in the scale: 7 Scale reliability coefficient:0.4530
The Shapiro-Wilk test is a statistical test used to determine whether a data set is normally distributed or not. It tests the null hypothesis that a sample comes from a normally distributed population. The test calculates a W statistic, which measures the degree of deviation from normality, and compares it to critical values to determine whether to reject or fail to reject the null hypothesis. A p-value is also calculated, which indicates the probability of obtaining the observed W statistic or a more extreme value if the null hypothesis is true. If the p-value is less than the significance level, the null hypothesis is rejected and the data is considered non-normal.
ShapiroBWWilk W test for normal data
Variable
Obs
W
V
Prob>z
y
18
0.894
2.325
1.689
0.046
z
x1 18 0.866 2.937 2.156 0.016
x2 18 0.923 1.693 1.054 0.146
x3 18 0.940 1.321 0.557 0.289
x4 18 0.825 3.841 2.694 0.004
x5 18 0.969 0.687 -0.753 0.774
x6 18 0.914 1.883 1.267 0.103
The Shapiro-Wilk test is a statistical test used to determine whether a data set is normally distributed or not. It tests the null hypothesis that a sample comes from a normally distributed population. The test calculates a W statistic, which measures the degree of deviation from normality, and compares it to critical values to determine whether to reject or fail to reject the null hypothesis. A p-value is also calculated, which indicates the probability of obtaining the observed W statistic or a more extreme value if the null hypothesis is true. If the p-value is less than the significance level (usually 0.05), the null hypothesis is rejected and the data is considered non-normal.
VIF 1/VIF
34.710 0.029
20.140 0.050
11.290 0.089
6.230 0.160
4.430 0.226
3.380 0.296
13.360
The VIF (Variance Inflation Factor) is a measure of how much the variance of the estimated regression coefficient is increased due to multicollinearity in the data. A VIF value of 1 indicates no multicollinearity, while values above 5 or 10 are often considered problematic. The 1/VIF column shows the degree to which the standard errors of the regression coefficients are reduced when the variable is removed from the model. In general, variables with high VIF values and low 1/VIF values should be considered for removal from the model to improve its accuracy and reduce multicollinearity. However, it is important to also consider the theoretical importance and relevance of each variable before removing them
from the model_
VIF_1/VIF_
1.950 0.513
1.880 0.532
1.610 0.622 1.810
..0.552
In this example, all variables have relatively low VIF values, indicating less multicollinearity in the model. The variable with the highest VIF value is 1.950, but its corresponding 1/VIF value of 0.513 suggests that removing this variable may not have a significant impact on reducing multicollinearity. The other variables have even lower VIF values and higher 1/VIF values, indicating their potential importance in the model. Overall, the model appears to have low levels of multicollinearity, which is a good indication for its accuracy and reliability.
We remove the variables x1,x2, and x4 from the model because these variables cause the problem of multicollinearity. According to the VIF analysis,
the value went above 10._
Conditional marginal effects Number of obs = 18 Model VCE: OLS
Expression: Linear prediction, predict()
dy/dx wrt: x3 x5 x6
At: x3 = 270.8503 (mean)
x5 = 140.9837 (mean)
x6 = 4365.344 (mean)
Delta-method
dy/dx std. err. t P>t [95% conf. interval]
x3 0.171 0.020 8.550 0.000 0.128 0.214
x5 -0.404 0.119 -3.390 0.004 -0.660 -0.148
x6 0.023 0.006 3.650 0.003 0.009 0.036
These conditional marginal effects show how the predicted value of the response variable changes when each predictor variable is increased by one unit, holding all other variables constant at their mean values. In this example, an increase of one unit in x3 (which has a mean value of 270.8503) is associated with an increase of 0.171 in the predicted value of the response variable. An increase of one unit in x5 (which has a mean value of 140.9837) is associated with a decrease of 0.404 in the predicted value of the response variable. And an increase of one unit in x6 (which has a mean value of 4365.344) is associated with an increase of 0.023 in the predicted value of the response variable. The standard errors, t-values, and p-values indicate whether these effects are statistically significant. In this case, the effect of x3 is highly significant (p<0.001), while the effects of x5 and x6 are also significant (p=0.004 and p=0.003, respectively). The confidence intervals provide a range of plausible values for the true effect sizes, based on the observed data. Overall, these results suggest that x3 has the strongest positive association with the response variable, while x5 has a negative association and x6 has a weaker positive association.
ShapiroBWWilk W test for normal data
Variable Obs W V z Prob>z
yhat 18 0.942 1.273 0.483 0.315
Based on the provided information, it appears that the Shapiro-Wilk W test was performed on a variable called "yhat" with 18 observations. The results show that the W statistic is 0.942 and the test statistic V is 1.273. The z-score is 0.483 and the p-value is 0.315. However, it is still unclear what "hist yhat,kdensity norm" refers to in relation to this information. It is possible that it could be related to the method or software used to perform the test, but more context is needed to provide a definitive answer.
Shapirob"Wilk W test for normal data
Variable Obs W V Z Prob>z
ehat 18 0.914 1.882 1.265 0.103
Based on the provided information, it appears that the Shapiro-Wilk W test was performed on a variable called "ehat" with 18 observations. The results show that the W statistic is 0.914 and the test statistic V is 1.882. The z-score is 1.265 and the p-value is 0.103. Again, it is unclear what "hist yhat,kdensity norm" refers to in relation to this information. It is possible that it could be related to the method or software used to perform the test, but more context is needed to provide a
definitive answer._
BreuschB^"Pagan/CookB^"Weisberg test for heteroskedasticity Assumption: Normal error terms Variable: Fitted values of y H0: Constant variance chi2(1) =0.64 Prob > chi2 = 0.4243
Linear regression
Lny Coef. St.Err. t- value P-value [95% Conf Interval] Sig
x3 .002 0 8.28 0 .0 .0
02 03 **
x5 -.005 .002 -3.10 .008 - -
.008 .001 ** x6 0 0 4.60 0 0 .0
01 **
Constant 2.792 .308 9.05 0 2. 3.
13 454 **
Mean dependent var 4.307 SD dependent var 0.319
R-squared 0.920 Number of obs 18
F-test 53.928 Prob > F 0.000
Akaike crit. (AIC)_-28.597 Bayesian crit. (BIC)_-25.035
*** p<.01, **p<.05, *p<.1
This is the output of a linear regression model with the dependent variable "lny" and four independent variables (x3, x5, x6, and a constant). The coefficients, standard errors, t-values, and p-values are provided for each independent variable. The results show that x3 and x6 have significant positive effects on the dependent variable at the 1% level, while x5 has a significant negative effect at the 5% level. The constant is also significant at the 1% level. The R-squared value indicates that the model explains 92% of the variation in the dependent variable. The F-test and associated p-value suggest that the overall model is significant at the 1% level. The Akaike and Bayesian information criteria (AIC and BIC) are measures of model fit that take into account both the goodness of fit and the complexity of the model. Lower values indicate better fit, and the values provided here suggest that this model fits well. The asterisks below each coefficient indicate the level of significance, with *** indicating significance at the 1% level, ** indicating significance at the 5% level, and * indicating significance at the 10% level.
Linear regression
Lny Coef. St.Err. t- value p- value [95% Conf Interval] Sig
x3 .002 0 8.78 0 .002 .003 ***
x5 -.005 .001 -3.72 .002 -.008 -.002 ***
x6 0 0 5.85 0 0 .001 ***
Constant 2.792 .225 12.38 0 2.308 3.276 ***
Mean dependent var R-squared F-test Akaike crit. (AIC) 4.307 0.920 104.982 -28.597 SD dependent var Number of obs Prob > F Bayesian crit. (BIC) 0.319 18 0.000 -25.035
*** p<.01, ** p<.05, * p<.1
This linear regression model estimates the relationship between the natural logarithm of the dependent variable (lny) and three independent variables (x3, x5, and x6). The coefficients for x3, x5, and x6 are 0.002, -0.005, and 0, respectively. The t-values for x3, x5, and x6 are 8.78, -3.72, and 5.85, respectively, with corresponding p-values of 0, 0.002, and 0. The constant term is 2.792 with a standard error of 0.225, a t-value of 12.38, and a p-value of 0. The R-squared
value for this model is 0.92, indicating that the independent variables explain 92% of the variation in the dependent variable. The F-test has a value of 104.982 with a p-value of 0, indicating that the model as a whole is statistically significant. The Akaike criterion (AIC) and Bayesian criterion (BIC) are -28.597 and -25.035, respectively. These values can be used to compare this model with other models to determine which one is the best fit for the data. The significance levels for the coefficients are indicated by asterisks (*). In this case, all three independent variables are statistically significant at the p<0.01 level.
Linear regression
Y Coef. St.Err. t- p- [95% Interval] Sig
value value Conf
x3 .171 .016 10.81 0 .137 .205 ***
x5 -.404 .107 -3.79 .002 -.632 -.175 ***
x6 .023 .006 4.02 .001 .011 .035 ***
Constant -10.135 17.349 -0.58 .568 -47.345 27.074
Mean dependent var 77.762 SD dependent var 23.352
R-squared 0.911 Number of obs 18
F-test 86.683 Prob > F 0.000
Akaike crit. (AIC) 127.875 Bayesian crit. (BIC) 131.436
*** p<.01, ** p<.05, * p<.1
Linear regression
Lny Coef. St.Err. t- p- [95% Interval] Sig
value value Conf
x3 .002 0 8.28 0 .002 .003 ***
x5 -.005 .002 -3.10 .008 -.008 -.001 ***
x6 0 0 4.60 0 0 .001 ***
Constant 2.792 .308 9.05 0 2.13 3.454 ***
Mean dependent var 4.307 SD dependent var 0.319
R-squared 0.920 Number of obs 18
F-test 53.928 Prob > F 0.000
Akaike crit. (AIC) -28.597 Bayesian crit. (BIC) -25.035
*** p<.01, ** p<.05, * p<.1
This linear regression model has three independent variables (x3, x5, and x6) that are all statistically significant at the p<0.01 level. The coefficients for x3, x5, and x6 are 0.002, -0.005, and 0, respectively. The R-squared value is 0.92, indicating that the independent variables explain 92% of the variation in the dependent variable. The F-test has a value of 104.982 with a p-value of 0, indicating that the model as a whole is statistically significant. The Akaike criterion (AIC) and Bayesian criterion (BIC) are -28.597 and -25.035, respectively, which can be used to compare this model with other models to determine which one is the best fit for the data.
Conditional marginal effects Number of obs = 18 Model VCE: OLS
Expression: Linear prediction, predict()
dy/dx wrt: x3 x5 x6
At: x3 = 270.8503 (mean)
x5 = 140.9837 (mean)
x6 = 4365.344 (mean)
_Delta-method_
dy/dx std. err. T P>t [95% conf.
_interval]
x3 0.002 0.000 8.280 0.000 0.002 0.003
x5 -0.005 0.002 -3.100 0.008 -0.008 -0.001
x6 0.000 0.000 4.600 0.000 0.000 0.001
This output shows the conditional marginal effects of the three independent variables (x3, x5, and x6) on the dependent variable, holding all other variables constant at their mean values. For example, for a one-unit increase in x3 (keeping x5 and x6 constant), the predicted value of the dependent variable increases by 0.002 units. The standard errors, t-values, and p-values are also provided to assess the significance of these effects. Overall, this model suggests that x3 has a positive effect on the dependent variable, while x5 has a negative effect. X6 does not appear to have a significant effect. However, it's important to keep in mind that these effects are conditional on the other variables being held constant at their mean values. The coefficients and effects may change if the values of the other variables change._
Variable Ols Robust Ln margins
x3 0.002*** 0 171*** 0.002*** 0.002***
x5 -0.005** -0.404** -0.005** -0.005**
x6 0.000*** 0.023** 0.000*** 0.000***
_cons 2.792*** -10.135 2.792*** 2.792***
Legend: * p<.05; ** p<.01; *** p<.001
Conclusion
The output shows the regression coefficients and associated statistics for a linear regression model. The "ols" column shows the coefficients estimated using ordinary least squares regression, while the "robust" column shows the coefficients estimated using a robust regression method that is less sensitive to outliers. The "ln" column shows the coefficients estimated using a logarithmic transformation of the dependent variable. The "margins" column shows the marginal effects of each independent variable on the dependent variable, holding
all other variables constant at their mean values. These effects are estimated using the "margins" command in Stata. The legend at the bottom of the output indicates the level of statistical significance for each coefficient, based on the p-value. A p-value less than.05 indicates that the coefficient is statistically significant at the 5% level, while a p-value less than.01 indicates significance at the 1% level, and so on. The most optimal models are OLS, margins, Ln models, because their p-value was 0.001. Thus, we can construct regression equations as follows. Linear regression model.
y=-10.135+0.002x3-0.404x5+0.023x6
1% increase in the import index increases the food production index by 0.002. 1% increase in the export volume decreases the food production index by
0.404. 1% increase in cereal yield increases the food production index by 0.023.
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