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Problem #1 An economic consulting firm was hired by a coffee producer. The coffee producer wanted the consulting firm to estimate the demand for its caffeinated coffee. The consulting firm and coffec producer agreed to estimate this demand curve using quarterly data over the period beginning 1982 through 2000 . The time-period entails 76 quarters of data. The consulting group decided to use the natural log form of the demand curve. The demand curve to be estimated took the following general form: LnQt=lnb0+b1lnPt+b2lnYt+b3Pts+b4T+b5D1+b6D2+b7D3 Where Qt= pounds of coffee consumed/person in quarter t. Pt= the price of coffee/pound in quarter t. Yt= Disposable income/person in quarter t. Pts= the price/lb of a substitute caffeinated beverage in quarter t. T= trend variable from 1982 quarter 1 to 2000 quarter 4 . D1=A dummy variable (binary variable) representing the 1st quarter (Jan - March). D2=A dummy variable (binary variable) representing the 2nd quarter (Apr-June). D3=A dummy variable (binary variable) representing the 3rd quarter (July - Sept). bk= the partial regression coefficients to be estimated. n=76 k=8 The following is the estimated regression equations with the calculated t-statistics in parenthesis. LnQ1=1.27890.1647lnPt+.5115lnYt+.1483Pts.0089T+.961D1.157D2.0097D3 (2.14) The following is the estimated regression equations with the calculated t-statistics in parenthesis. R2=.8256F=45.9849 a. Interpret the coefficient of determination, R2. b. Interpret the estimated coefficient on price of coffee, Pt. c. Interpret the estimated coefficient on disposable income, Yt. d. Interpret the estimated coefficient on the price of substitute goods, Pts. e. Interpret the time Ttrend estimated coefficient. f. The dummy variables (Dt) illustrate the seasonality of coffee demand. Given the coefficients on the dummy variables what can you say about seasonality of coffee demand? g. Are the estimated coefficient on Pt,It,Pt2 and t statistically significant using a 2-tailed test given the level of significance =0.05(5.0%) ? Explain. h. Test the hypothesis that the R2 is statistically significant? Set =0.05(5%). Problem #1 An economic consulting firm was hired by a coffee producer. The coffee producer wanted the consulting firm to estimate the demand for its caffeinated coffee. The consulting firm and coffec producer agreed to estimate this demand curve using quarterly data over the period beginning 1982 through 2000 . The time-period entails 76 quarters of data. The consulting group decided to use the natural log form of the demand curve. The demand curve to be estimated took the following general form: LnQt=lnb0+b1lnPt+b2lnYt+b3Pts+b4T+b5D1+b6D2+b7D3 Where Qt= pounds of coffee consumed/person in quarter t. Pt= the price of coffee/pound in quarter t. Yt= Disposable income/person in quarter t. Pts= the price/lb of a substitute caffeinated beverage in quarter t. T= trend variable from 1982 quarter 1 to 2000 quarter 4 . D1=A dummy variable (binary variable) representing the 1st quarter (Jan - March). D2=A dummy variable (binary variable) representing the 2nd quarter (Apr-June). D3=A dummy variable (binary variable) representing the 3rd quarter (July - Sept). bk= the partial regression coefficients to be estimated. n=76 k=8 The following is the estimated regression equations with the calculated t-statistics in parenthesis. LnQ1=1.27890.1647lnPt+.5115lnYt+.1483Pts.0089T+.961D1.157D2.0097D3 (2.14) The following is the estimated regression equations with the calculated t-statistics in parenthesis. R2=.8256F=45.9849 a. Interpret the coefficient of determination, R2. b. Interpret the estimated coefficient on price of coffee, Pt. c. Interpret the estimated coefficient on disposable income, Yt. d. Interpret the estimated coefficient on the price of substitute goods, Pts. e. Interpret the time Ttrend estimated coefficient. f. The dummy variables (Dt) illustrate the seasonality of coffee demand. Given the coefficients on the dummy variables what can you say about seasonality of coffee demand? g. Are the estimated coefficient on Pt,It,Pt2 and t statistically significant using a 2-tailed test given the level of significance =0.05(5.0%) ? Explain. h. Test the hypothesis that the R2 is statistically significant? Set =0.05(5%)