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 perform some statistical analysis based on the given information.
i) To determine if the individual partial slope coefficients are statistically significant, we can examine the t-ratios associated with each coefficient. If the absolute value of the t-ratio is greater than 2 (or you can choose a different threshold based on your desired significance level), then the coefficient is considered statistically significant.
For Model I:
- The t-ratio for Pc is 45.467, which is greater than 2, indicating that the coefficient is statistically significant.
- The t-ratio for Pb is 13.44, which is also greater than 2, indicating that the coefficient is statistically significant.
- The t-ratio for Pf is 20.245, which is greater than 2, indicating that the coefficient is statistically significant.
- The t-ratio for Y is 0.154, which is less than 2, indicating that the coefficient is not statistically significant.
For Model II:
- The t-ratio for Pc is 22.8, which is greater than 2, indicating that the coefficient is statistically significant.
- The t-ratio for Y is 0.077, which is less than 2, indicating that the coefficient is not statistically significant.
ii) To determine if the prices of chicken, beef, fish, and income simultaneously influence the demand for chicken, we can use the coefficient of determination (R-squared) value. If the R-squared value is close to 1 (typically above 0.7), then the variables collectively have a significant influence on the demand for chicken.
For Model I, the R-squared value is 0.98, indicating that 98% of the variation in chicken demand is explained by the prices of chicken, beef, fish, and income.
For Model II, the R-squared value is 0.99, indicating that 99% of the variation in chicken demand is explained by the prices of chicken and income.
iii) To determine if the prices of beef and fish are the same, we need to examine the covariance between the prices of beef and fish. If the covariance is zero, then the prices are considered independent, and if the covariance is non-zero, then the prices are considered dependent. In this case, the covariance between prices of beef and fish is 112.54, indicating that there is a non-zero covariance. Therefore, we can conclude that the prices of beef and fish are not the same and are influenced by each other.
iv) To determine if the prices of beef and fish jointly influence the quantity of chicken demand, we can examine the coefficients of Model I. Based on the model equation, the coefficient for Pb is -9.86 and the coefficient for Pf is 39.8. Since these coefficients are non-zero, we can say that the prices of beef and fish (jointly) do influence the quantity of chicken demand.
Overall, based on the given information and analysis, the individual partial slope coefficients are statistically significant, the prices of chicken, beef, and fish, along with income, collectively influence the demand for chicken, the prices of beef and fish are not the same, and the prices of beef and fish (jointly) influence the quantity of chicken demand.