Discuss the statistical significance of the parameter estimates aˆ, bˆ, cˆ, and dˆ using the p-values. Are the signs of bˆ, cˆ and dˆ consistent with the theory of demand?

To discuss the statistical significance of the parameter estimates aˆ, bˆ, cˆ, and dˆ using p-values, you would typically be referring to the coefficients of a regression model. The p-values associated with these coefficients can provide insights into whether or not their estimates are statistically significant.

Here's how you can determine the statistical significance of these parameter estimates using p-values:

1. Run a regression model: Start by running the regression model using the appropriate statistical software or programming language. The regression model will have one or more independent variables (predictors) and a dependent variable (outcome). In this case, you seem to be interested in demand, so the dependent variable could represent demand, while the independent variables could be the coefficients aˆ, bˆ, cˆ, and dˆ.

2. Calculate p-values: Once the regression model is run, the software will calculate the p-values associated with each coefficient. The p-value represents the probability of observing a coefficient as extreme as the estimate if the null hypothesis is true. In this case, the null hypothesis would state that there is no relationship between the independent variables and the dependent variable.

3. Interpret the p-values: Typically, a significance level (often denoted as α) is chosen as a threshold to determine statistical significance. Commonly used significance levels are 0.05 or 0.01. If the p-value for a coefficient is lower than the chosen significance level, it is considered statistically significant, indicating that the coefficient is unlikely to be zero. Conversely, if the p-value is higher than the significance level, the coefficient is considered not statistically significant, suggesting that it might not differ significantly from zero.

Regarding the signs of bˆ, cˆ, and dˆ being consistent with the theory of demand, it would depend on the specific theory and context. However, in demand analysis, the signs of coefficient estimates are often expected to align with economic theory. For example, a positive coefficient for the price variable (bˆ) might indicate that demand decreases as price increases, which would be consistent with the law of demand. Similarly, the signs of other relevant coefficients (cˆ and dˆ) would need to align with expected relationships according to demand theory.

In summary, you can assess the statistical significance of parameter estimates by examining the associated p-values. Additionally, you can evaluate whether the signs of the coefficients align with the theory of demand to determine if the results are consistent with expectations.