Analysis of Chicken Meat Demand
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1. Introduction
The given data represents the chicken meat demand over the time period of several years from 1980 to 2014 in a certain company who is producing chicken meat to the market. In today’s competitive market chicken meat demand is depend on many external factors or determinants. Several determinants of them are
 Income of the consumers.
 Other substitutes in the market check as other meats like port, beef, mutton and port or fish and seafood.
 Price of the chicken in the market
 Number of competitors in the market who produce chicken meat to the market
 Other factors such as health hazards link to chicken meat such as bird flu outbreaks.
Other than to these main determinants, the demand could vary seasonally with even one single year, but given data is not supported to analyze seasonal variances.
So as a chief analyst, this given data study is analyzed and investigated to show the given determinants are really significantly affected to the chicken demand produced by this company where this data is collected.
Also the interpretation is based on the assumption that this data is collected in scientifically and no bias in data sample.
The assumption regarding the data set given for analysis:
Assume,
Y stands for : Chicken meat demand
PC Stands for : Price of chicken meat
PB stands for : Price of beef
PR stands for : Future price of chicken
YD stands for : Consumer income
2. Literature Review
Demand for any consumer good, whatever irrespective of chicken meat or any other in the market is the quantity consumers are willing and able to purchase during period of time. Although the price is the main factor affecting the demand, economist emphasizes magnitude of other factors that effect for the quantity consumers buying. However, indeed only six factors are considered sufficiently important in studies of market demand.
 P = Price of the good
 M =Consumer’s income
 Pr = Price of related goods
 T =Taste pattern of the consumer
 Pe = Expected future price of the good
 N =Number of consumers in the market
The following equation is an example of linear form of the general demand function.
Q = a + bP + cM + dPr + eT + fPe + gN
a,b,c,d,e,f and g are called slope parameters, they measure the effect of quantity demanded of changing one of the variables, while holding other variables as constant.
3. Methodology and the Modal
3.1 The multiple regression modal
In statistics, regression analysis is a statistical process for estimating the relationships among variables. It includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables. More specifically, regression analysis helps one understand how the typical value of the dependent variable changes when any one of the independent variables is varied, while the other independent variables are held fixed. Most commonly, regression analysis estimates the conditional expectation of the dependent variable given the independent variables – that is, the average value of the dependent variable when the independent variables are fixed. In all cases, the estimation target is a function of the independent variables called the regression function. In regression analysis, it is also of interest to characterize the variation of the dependent variable around the regression function which can be described by a probability distribution.
The coefficients of the multiple regression model are estimated using sample data.
Multiple regression equation with K independent variables is as below.
So the chicken demand function can be expressed as follows
Y = β_{0} + β_{1}PC+ β_{2}PB+ β_{3}PR + β_{4}YD
So, a = β_{0} , b= β_{1 } etc ….
Then given data is fed to the SPSS and relevant reports are taken. In the next section, of the report detailed analysis is given according to the different analysis methods.
4. Correlation Matrix
Correlations 

Y 
PC 
PB 
PR 
YD 

Y 
Pearson Correlation 
1 
.122 
.989^{**} 
.076 
.933^{**} 
Sig. (2tailed) 
.485 
.000 
.666 
.000 

Sum of Squares and Crossproducts 
116907.336 
568.130 
31605.725 
348.947 
36612.792 

Covariance 
3438.451 
16.710 
929.580 
10.263 
1076.847 

N 
35 
35 
35 
35 
35 

PC 
Pearson Correlation 
.122 
1 
.059 
.994^{**} 
.258 
Sig. (2tailed) 
.485 
.736 
.000 
.135 

Sum of Squares and Crossproducts 
568.130 
185.439 
75.185 
182.791 
402.728 

Covariance 
16.710 
5.454 
2.211 
5.376 
11.845 

N 
35 
35 
35 
35 
35 

PB 
Pearson Correlation 
.989^{**} 
.059 
1 
.007 
.928^{**} 
Sig. (2tailed) 
.000 
.736 
.969 
.000 

Sum of Squares and Crossproducts 
31605.725 
75.185 
8741.723 
8.512 
9960.241 

Covariance 
929.580 
2.211 
257.109 
.250 
292.948 

N 
35 
35 
35 
35 
35 

PR 
Pearson Correlation 
.076 
.994^{**} 
.007 
1 
.207 
Sig. (2tailed) 
.666 
.000 
.969 
.233 

Sum of Squares and Crossproducts 
348.947 
182.791 
8.512 
182.207 
320.896 

Covariance 
10.263 
5.376 
.250 
5.359 
9.438 

N 
35 
35 
35 
35 
35 

YD 
Pearson Correlation 
.933^{**} 
.258 
.928^{**} 
.207 
1 
Sig. (2tailed) 
.000 
.135 
.000 
.233 

Sum of Squares and Crossproducts 
36612.792 
402.728 
9960.241 
320.896 
13178.387 

Covariance 
1076.847 
11.845 
292.948 
9.438 
387.600 

N 
35 
35 
35 
35 
35 

**. Correlation is significant at the 0.01 level (2tailed). 

According the Pearson correlation, there is a high correlation between chicken meat demand (Y) and price of the beef (PB). The Pearson correlation value is 0.989.
Also same high level of correlation value is seen between chicken meat demand (Y) and the consumer’s income (YD). The Pearson correlation value is 0.933.
There is no direct relationship in future chicken price (PR) and chicken market price (PC) for the chicken demand (Y) as seen in the correlation matrix, Pearson correlation values are low. Respective correlation values are 0.122 and 0.076 respectively.
Only the relation between the demand and other variables are specially mentioned above, but the multiple relations between other independent variables also can be interpreted as shown in the matrix.
5. Comparison of Regressions
5.1 Descriptive statistics
Descriptive Statistics 

N 
Range 
Minimum 
Maximum 
Mean 
Std. Deviation 

Statistic 
Statistic 
Statistic 
Statistic 
Statistic 
Std. Error 
Statistic 

Y 
35 
175.33 
20.22 
195.55 
84.7237 
9.91168 
58.63831 

PC 
35 
8.90 
6.80 
15.70 
10.2343 
.39475 
2.33540 

PB 
35 
55.36 
23.25 
78.61 
45.9011 
2.71035 
16.03463 

PR 
35 
8.80 
7.10 
15.90 
10.6743 
.39130 
2.31496 

YD 
35 
56.60 
18.00 
74.60 
44.2514 
3.32780 
19.68755 

Valid N (listwise) 
35 

By looking in to the descriptive statistics we can say that mean of the mean chicken demand is 84.72 and has a high variation in mean (std 58.63). Mean chicken price is 10.23 and it has a low variance. (std 2.33). Mean beef price is 45.9 and has a moderate variance (Std. 16.03). Consumer’s income mean value is 44.25 and it has a moderate variance (std = 19.68)
5.2 Discussion of the coefficient
Model Summary 

Model 
R 
R Square 
Adjusted R Square 
Std. Error of the Estimate 
1 
.993^{a} 
.985 
.983 
7.60224 
a. Predictors: Constant, Y, PR, PB, PC 

Adjusted R Square is 0.983. It implies that 98.3 % of the variation in chicken meat demand is explained by the variation in PC, PB, PR and YD, taking in to account the sample size and number of independent variables.
5.3 ANOVA
ANOVA^{a} 

Model 
Sum of Squares 
df 
Mean Square 
F 
Sig. 

1 
Regression 
115173.515 
4 
28793.379 
498.207 
.000^{b} 
Residual 
1733.821 
30 
57.794 

Total 
116907.336 
34 

b. Predictors: Constant,Y,PR, PB, PC Hypothesis: H_{0 :} β_{1} = β_{2} = β_{3} = β_{4} = 0 H_{1 :} β_{1} , β_{2} , β_{3} , β_{4} at least one not zero. F value for this sample test is 498.207 with 4 and 30 degrees of freedom. Critical value of the F stat from the F table with α = 0.05 is 5.7459. So calculated F stat 498.207 > 5.7459. SO we reject H_{0.} So there is evidence that at least one independent variable effects Y. 

5.4 Are individual variables significant?
Coefficients^{a} 

Model 
Unstandardized Coefficients 
Standardized Coefficients 
t 
Sig. 

B 
Std. Error 
Beta 

1 
(Constant) 
109.410 
10.075 
10.860 
.000 

PR 
14.986 
6.136 
.597 
2.442 
.021 

PB 
3.612 
.254 
.988 
14.206 
.000 

PR 
16.600 
6.150 
.655 
2.699 
.011 

YD 
.102 
.212 
.034 
.481 
.634 

a. Dependent Variable: Demand 

The pvalue for each term tests the null hypothesis that the coefficient is equal to zero (no effect). A low pvalue (< 0.05) indicates that that can reject the null hypothesis. So in this chicken meat analysis, PR ,PB and PR are statistically significant since the p value of these are less than 0.05. So there we can reject the null hypothesis and implies that significance relationship is there for the chicken meat demand other dependent variables PR,PB and PR.
Income is not statistically significant according to the analysis.
6. Conclusion
The empirical findings show that the demand for chicken meat demand is affected by the variation in the price Of Chicken (PB), price Of Beaf(PB) and price Of Future(PR).
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