The following two models were estimated to analyze the demand for chicken around
Mzumbe university campus.
I.Qc = 43.310 –15.298Pc –9.86Pb + 39.8Pf + 1.87Y
Where Qc = quantity of chicken demanded in 2012.
Pc=price ofchicken.
Pb = price of beef.
Pf = price of fish.
Y=income.
aAre induvidual partial slope coefficients are statistically significant? Show your working clearly
To determine if the individual partial slope coefficients in the given model are statistically significant, we need to perform hypothesis tests.
The null hypothesis (H0) is that the coefficient is equal to zero, indicating that the variable has no effect on the demand for chicken. The alternative hypothesis (Ha) is that the coefficient is not equal to zero, indicating that the variable does have an effect on the demand for chicken.
For each variable (Pc, Pb, Pf, and Y), we will perform a t-test. The t-test will calculate the t-statistic value, which we can compare with the critical t-value to see if the coefficient is statistically significant.
Step 1: Calculate the t-statistic
To calculate the t-statistic, we need the following information:
- Coefficient value (from the regression model)
- Standard error of the coefficient (also from the regression model)
Step 2: Determine the critical t-value
The critical t-value depends on the desired significance level (e.g., 0.05 or 0.10) and the degrees of freedom (n - k - 1), where n is the sample size and k is the number of independent variables.
Step 3: Compare the t-statistic with the critical t-value
If the absolute value of the t-statistic is greater than the critical t-value, then the coefficient is considered statistically significant. If not, we fail to reject the null hypothesis and conclude that the coefficient is not statistically significant.
Note: In the t-test, if the p-value corresponding to the t-statistic is less than the desired significance level (e.g., p < 0.05), then we can also conclude that the coefficient is statistically significant.
Now, you need to provide the coefficient values and standard errors for each variable (Pc, Pb, Pf, and Y) to calculate the t-statistic and check for statistical significance.