## 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 |
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Y | PC | PB | PR | YD | ||

Y | Pearson Correlation | 1 | .122 | .989^{**} |
.076 | .933^{**} |

Sig. (2-tailed) | .485 | .000 | .666 | .000 | ||

Sum of Squares and Cross-products | 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. (2-tailed) | .485 | .736 | .000 | .135 | ||

Sum of Squares and Cross-products | 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. (2-tailed) | .000 | .736 | .969 | .000 | ||

Sum of Squares and Cross-products | 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. (2-tailed) | .666 | .000 | .969 | .233 | ||

Sum of Squares and Cross-products | 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. (2-tailed) | .000 | .135 | .000 | .233 | ||

Sum of Squares and Cross-products | 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 (2-tailed). | ||||||

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 |
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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 |
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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} |
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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 | ||||

- Dependent Variable: Demand
b. Predictors: Constant,Y,PR, PB, PC Hypothesis: H H 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 So there is evidence that at least one independent variable effects Y. |
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## 5.4 Are individual variables significant?

Coefficients^{a} |
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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 p-value for each term tests the null hypothesis that the coefficient is equal to zero (no effect). A low p-value (< 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).