3.(2+3 5 pt) Consider the binary variable Y defined for individual family homes in the USA which is 1 if the home has a solar heating system, and 0 if it does not. A researcher has used LOGIT to examine how Y depends on the assessed value of the home X (unit =$100,000), and whether the home is the Western USA or not (D = 1 if the home is in the Western USA, and D = 0 if not). A standard LOGIT model is used where P(Y = 1|I) = 1/(1 + e*) where the indicator function I is given by: 1 I = Bo 1 D + 2 X + 3 DX 3.(a) State the following null hypothesis in terms of the parameters of the model: If a home is in the Western USA, then home price has no effect on the probability that the home has a solar heating system. = 0 3.(b) Suppose the researcher obtained a random sample of homes and estimated several Logit models. Results are given below: Model Dependent Variable Independent Ln L Variable(s) 1 Y D, X, DX -140 2 Y -156 3 Y X -150 4 Y D, X -144 5 Y D, DX -148 6 Y X, DX -146 At a 99% level of confidence, test the null hypothesis that = 3 = 0 against the alternative hypothesis that at least one of and 3 is not zero. (Show work)