For each hypothesis testing, state the null and alternative, the test statistic, the critical value, your conclusion and your interpretation. Consider significance level u=0.05. Please also use at least two decimals in your calculations. Demand for Coffee Suppose you are employed by a coffee producer and asked to determine the demand function for it. The company is interested in determinants of coffee demand except for its own price. A group of marketing researchers propose the following specification: C = do + In Y+a, In PT +e Another group of researchers propose the following specification: C = Bo +BY+B,PT + u where Y is the income level of consumers, PT is the price of tea, and the level of coffee consumption. An employee of the company gathered appropriate data and provided following estamation results. SSR= Sum of Squares Residuals. EC-C)' = 263.44 (InC) = 2.58. N=85, (Y-PT) = = 37.4 Model 1: C = 27.52+1.32Y +2.44 PT RP=0.38, SSR=113.44, Cov (B, B.,) = -0.005 Model 2: In C =1.18+ 0.39 In Y + 0.63 In PT R?=0.31, SSR =15.67, Cov (@j)=-0.003 Model 3: e= -2.87-0.86 In Y+1.08 In PT R?=0.23, SSR=9.3, Var(In Y) = 2.99 Model 4: Y = 3.92+2.65 In PT R?=0.12, SSR=28.75, Var(PT) = 10.53 n 10.08 0.23 0.41 0.15 0.14 0.12 1.74 0.61 0.46 15 06 132 1.41 2.77 0.05 0.1 0.8 Model 8: Inc=0.87+3.66 +5.08(In Y) +0.441n' +7,55PT R?=0.26, SSR=17.6. Cov,Y)= 0.001 Model 9: In PT = 4.98-1.25 In Y R?=0.45, SSR=18.25, Var(InPT) = 7.21 2.26 0.38 1) Are findings of Model 1 consistent with economic theory? Why/Why not? Provide description of relevant theory and statistical evidence for your answer! 2) Erdener thinks that if price of tea rises by 10%, then coffee consumption will rise by 5%. Can you statistically test this hypothesis by using estimation results given above? If YES, provide your answer with details. If NO, state what additional information you would need. 3) Ataman thinks that sum of elasticities of coffee consumption with respect to income and price of tea should be one, i.e. + = 1. Can you statistically test this hypothesis by using the estimation results given above? If YES, provide your answer with details. If NO, state what additional information you would need. 4) A friend of yours states that coffee consumption should be inelastic with respect to income and elastic with respect to price of tea. Can you test these claims? Why/Why not? Explain your answer and provide statistical evidence 5) The manager of the company has Mathematics major and likes logarithm functions very much. Thus, she wants to use the double log model. Do these results support the log-log model compared to linear model? Provide statistical evidence for your answer! 6) Erdener thinks that error terms of both Model 1 and Model 2 may not be constant. How would you respond to Erdener given estimation results above? Conduct appropriate econometric tests and provide evidence. Name and justify your choices of tests conducted with all the details. 7) Jlide Yldrm thinks that there will be serious multicollinearity in the models. Given estimation results above, do you agree with her? Explain your reasoning and provide statistical evidence for your answer. 8) A friend of yours wants to add advertisement level (A) into logarithmic model and apply original White test for this new multiple regression model. Write down theoretical regression equations for new logarithmic model and corresponding White test model. 9) Calculate an estimate for the correlation coefficient of the linear relationship between consumption level (C) and income level (Y). Conduct a test for significance of the correlation. Interpret your findings. For each hypothesis testing, state the null and alternative, the test statistic, the critical value, your conclusion and your interpretation. Consider significance level u=0.05. Please also use at least two decimals in your calculations. Demand for Coffee Suppose you are employed by a coffee producer and asked to determine the demand function for it. The company is interested in determinants of coffee demand except for its own price. A group of marketing researchers propose the following specification: C = do + In Y+a, In PT +e Another group of researchers propose the following specification: C = Bo +BY+B,PT + u where Y is the income level of consumers, PT is the price of tea, and the level of coffee consumption. An employee of the company gathered appropriate data and provided following estamation results. SSR= Sum of Squares Residuals. EC-C)' = 263.44 (InC) = 2.58. N=85, (Y-PT) = = 37.4 Model 1: C = 27.52+1.32Y +2.44 PT RP=0.38, SSR=113.44, Cov (B, B.,) = -0.005 Model 2: In C =1.18+ 0.39 In Y + 0.63 In PT R?=0.31, SSR =15.67, Cov (@j)=-0.003 Model 3: e= -2.87-0.86 In Y+1.08 In PT R?=0.23, SSR=9.3, Var(In Y) = 2.99 Model 4: Y = 3.92+2.65 In PT R?=0.12, SSR=28.75, Var(PT) = 10.53 n 10.08 0.23 0.41 0.15 0.14 0.12 1.74 0.61 0.46 15 06 132 1.41 2.77 0.05 0.1 0.8 Model 8: Inc=0.87+3.66 +5.08(In Y) +0.441n' +7,55PT R?=0.26, SSR=17.6. Cov,Y)= 0.001 Model 9: In PT = 4.98-1.25 In Y R?=0.45, SSR=18.25, Var(InPT) = 7.21 2.26 0.38 1) Are findings of Model 1 consistent with economic theory? Why/Why not? Provide description of relevant theory and statistical evidence for your answer! 2) Erdener thinks that if price of tea rises by 10%, then coffee consumption will rise by 5%. Can you statistically test this hypothesis by using estimation results given above? If YES, provide your answer with details. If NO, state what additional information you would need. 3) Ataman thinks that sum of elasticities of coffee consumption with respect to income and price of tea should be one, i.e. + = 1. Can you statistically test this hypothesis by using the estimation results given above? If YES, provide your answer with details. If NO, state what additional information you would need. 4) A friend of yours states that coffee consumption should be inelastic with respect to income and elastic with respect to price of tea. Can you test these claims? Why/Why not? Explain your answer and provide statistical evidence 5) The manager of the company has Mathematics major and likes logarithm functions very much. Thus, she wants to use the double log model. Do these results support the log-log model compared to linear model? Provide statistical evidence for your answer! 6) Erdener thinks that error terms of both Model 1 and Model 2 may not be constant. How would you respond to Erdener given estimation results above? Conduct appropriate econometric tests and provide evidence. Name and justify your choices of tests conducted with all the details. 7) Jlide Yldrm thinks that there will be serious multicollinearity in the models. Given estimation results above, do you agree with her? Explain your reasoning and provide statistical evidence for your answer. 8) A friend of yours wants to add advertisement level (A) into logarithmic model and apply original White test for this new multiple regression model. Write down theoretical regression equations for new logarithmic model and corresponding White test model. 9) Calculate an estimate for the correlation coefficient of the linear relationship between consumption level (C) and income level (Y). Conduct a test for significance of the correlation. Interpret your findings