A property agent believes that there is possibility of interaction effects between X,, size of house (thousand square ft) and X2 , house type (A =1,B =0)on the Y , house price (RM thousand). Hence, he fit the regression model , Y, = B + B,X,, + B2X,2 + B,X,, X,2 + 8, where E()=0, o(,,&, )=0 for i # j , and var()= 2. The following results using SAS Enterprise Guide was obtained: Sum of Mean Source DF Squares Square F Value Model 3 9120.46367 3040.15456 30.05 Error 42 4248.84068 101.16287 Corrected Total 45 13369 Parameter Standard Variable DF Estimate Error Intercept 158.49125 18.12589 XI 1.14161 0.21480 X2 0.44200 0.49197 XIX2 13.47016 3.09966 a) Test at a = 0.05 whether the model is significant. (2 marks) b) Determine whether the interaction term can be dropped from the model. (3 marks) C) Estimate the price for the two different house types when the size of the house is 1200 square ft. (3 marks) d) Sketch two functions to depict the estimated mean price for the two house types in a single graph. (4 marks) e) State the point estimate of ,. Discuss on how do we interpret its meaning in the context of this