ECMT 5001 Year 2008 Semester 2_ECMT 5001 Solution Tutorial 9.docVIP

Econometrics Business Statistics ECMT5001: Principles of Econometrics Tutorial 9: Multiple Regression Applications NOTE: Use EViews to solve the computational exercises. The following fitted models are based on 11 annual observations: Model A Model B (Estimated standard errors are given in parentheses) The variables are: Y - per capita number of cups of coffee consumed per day X - price of coffee A$ per 500gram packet. Interpret the slope coefficients in the two estimated models Model A: On average, all else held constant, a $1 increase in the price of coffee (per 500 gr packet) will decrease the number of cups consumed per day by 0.48. Model B: in a model where both X and Y are logged, the slope coefficient is the elasticity. We say that, for a 1% increase in the price of coffee, there will be a 0.25% decrease in the number of cups consumed per day Evaluate the price elasticities of demand for coffee in the two models. (For the appropriate model, evaluate the elasticity at the point of the means .) The elasticity at the means is defined by: Model A: Model B: ε = -0.2530 Test the hypotheses that the slope coefficients are equal to zero in each case. Model A: H0: βA = 0 H1: βA ≠ 0 Level of Significance: α = 0.05 Distribution: . Assuming that the ui ~ iidN(0,σ2 ){ i.e. there is no serial correlation, no heteroskedasticity and E(error|Xi)=0} and assuming all other assumptions are met. (Recall that k is the number of regression coefficients estimated!) Critical Value: from the t-tables, the 5% critical value with 11 – 2 = 9 degrees of freedom is 2.262 for a two-tail test. Rejection Rule: Reject H0 if t* is greater than 2.262 or less than -2.262. Calculated Value: t* = -0.479/0.114 = -4.21. Conclusion: Since t* is less than the critical value, we reject H0 and we reject the null hypothesis at the 5% level. Conclude that, the evidence supports a negative linear relationship between the price of coffee and the numb