Suppose you have the following estimated regressions for coffee consumption with 123 observations. Modell: C 2.43-1.22 P+2.35Y R2=0.48 (1.1) (0.18) (0.65) Model 2: C 1.85-1.07 P+1.98Y+0.42 PT R=0.59 (1.3) (0.13) (0.54) (0.16) Model 3: C 2.97-1.38 P R=0.39 (1.2) (0.13) Model 4:C=1.24-0.87 P+1.48Y+0.32 PT-0.18 PM R=0.60 (1.1) (0.20) (0.44) (0.13) 0.99 Where P is price index for coffee, Y represents the income index, PT is the price of tea, PM represents price of milk and C represents the cups of coffee consumed. You are also given that C=5,Y=1750, P=8, PT=1.5,PM = 3.5. a) Consider Model 4, are these results consistent with economic theory? Explain your answer with statistical evidence. b) Can you test the overall significance for effects of price of coffee, income and price of tea on coffee demand? If YES, provide test result. If NO, explain your reasoning. c) Use an F-test approach to Test the following hypotheses. i) Price of milk and price of tea jointly affects the demand for coffee. ii) Income does not affect the demand for coffee. iii) Price of milk, income and price of tea jointly affects the demand for coffee. iv) Price of milk does not affect the demand for coffee. d) Do you agree with inclusion of price of milk in the regression estimations? Suggest other variables to be included in the demand line of coffee. Justify your answer. e) Is coffee an inferior good? Support your answer with statistical evidence. f) Can you determine the price elasticity of demand for coffee? If YES, provide test result. If NO, explain your reasoning. g) Are coffee and tea substitutes? Support your answer with statistical evidence. h) Suppose that a researcher estimates Model 1 with a dependent variable of CT which is measured in 10 cups of coffee. Write down the results obtained by the researcher.