The following two models were estimated to analyze the demand for chickenaround
Mzumbe university campus.
I. Qc = 43.310 – 15.298Pc – 9.86Pb + 39.8Pf + 1.87Y.
(3.05) (45.467) (13.44) (20.245) (0.154)
R-square= 0.98
II.
Qc = -17.288 + 61.138Pc + 2.046Y.
(1.92) (22.8) (0.077)
R-square = 0.99
Where Qc = quantity of chicken demanded in 2012.
Pc = price of chicken.
Pb = price of beef.
Pf = price of fish.
Y = income.
The variances of Prices of beef and fish are respectively 180.49 and 409.87, and their
covariance is 112.54. Figures in parenthesis are t-ratios.
Required:
i) Are the individual partial slope coefficients statistically significant?
ii) Do the prices of chicken, beef and fish and income simultaneously influence
demand for chicken?
iii) It was stipulated that the prices of beef and fish are the same. Do you agree with
this statement, why?
iv) Do the prices of beef and fish (jointly) influence quantity of chicken demand?
To answer these questions, we need to analyze the given regression models and their statistics. Specifically, we will look at the t-ratios and the R-square values.
i) To determine if the individual partial slope coefficients are statistically significant, we look at the t-ratios. A t-ratio greater than 2 (in absolute value) generally indicates statistical significance.
For Model I:
- Partial slope coefficient for Pc: -15.298 / 45.467 = -0.336 (t-ratio: 3.05)
- Partial slope coefficient for Pb: -9.86 / 13.44 = -0.734 (t-ratio: 45.467)
- Partial slope coefficient for Pf: 39.8 / 20.245 = 1.962 (t-ratio: 13.44)
- Partial slope coefficient for Y: 1.87 / 0.154 = 12.143 (t-ratio: 20.245)
For Model II:
- Partial slope coefficient for Pc: 61.138 / 22.8 = 2.68 (t-ratio: 1.92)
- Partial slope coefficient for Y: 2.046 / 0.077 = 26.598 (t-ratio: 0.077)
Based on the t-ratios, the partial slope coefficients for both models are statistically significant, except for the slope coefficient for Pc in Model II.
ii) To determine if the prices of chicken, beef, fish, and income simultaneously influence demand for chicken, we look at the R-square values. R-square represents the proportion of variance in the dependent variable that can be explained by the independent variables.
For Model I, R-square = 0.98, indicating that 98% of the variation in chicken demand can be explained by the given independent variables (price of chicken, beef, fish, and income).
For Model II, R-square = 0.99, indicating that 99% of the variation in chicken demand can be explained by the given independent variables (price of chicken and income).
Based on the high R-square values, we can conclude that the prices of chicken, beef, fish, and income simultaneously influence the demand for chicken in both models.
iii) To determine if the prices of beef and fish are the same, we need to compare their covariance with their individual variances. If the covariance is close to zero and the variances are similar, it suggests that the prices of beef and fish are the same.
Given:
- Variance of Pb = 180.49
- Variance of Pf = 409.87
- Covariance of Pb and Pf = 112.54
The covariance of 112.54 is relatively large compared to the variances. Therefore, we can conclude that the prices of beef and fish are not the same.
iv) To determine if the prices of beef and fish (jointly) influence the quantity of chicken demand, we need to consider the regression models. In Model I, the partial slope coefficient of Pf is statistically significant, indicating that the price of fish has a significant impact. Similarly, in Model II, the partial slope coefficient of Pc is statistically significant, indicating that the price of chicken has a significant impact. However, since the joint influence is not explicitly mentioned or modeled, we cannot directly conclude if the prices of beef and fish (jointly) influence the quantity of chicken demand.