Is there a difference between the average sale price of "Excellent" vs. "Good" apartment buildings? To answer this question, first we need to generate a new variable that is the sale price divided by the number of apartments in the building (so that we can compare different sizes of apartment buildings). After doing this, conduct a hypothesis test for the average of this variable, allowing for at most a 1% Type I error, and be sure to clearly state your hypotheses, conclusions, and possible error in plain language.

SalePrice	Apartments	Age	LotSize	ParkSpaces	BldArea	Condition	APTSIZE
90300	4	82	4365	0	4266	F	21.16737
384000	20	13	17798	0	14391	G	26.68334
157500	5	66	5913	0	6615	G	23.80952
676200	26	64	7750	6	34144	E	19.80436
165000	5	55	5150	0	6120	G	26.96078
300000	10	65	12506	0	14552	G	20.61572
108750	4	82	7160	0	3040	G	35.77303
276538	11	23	5120	0	7881	G	35.0892
420000	20	18	11745	20	12600	G	33.33333
950000	62	71	21000	3	39448	G	24.08234
560000	26	74	11221	0	30000	G	18.66667
268000	13	56	7818	13	8088	F	33.13551
290000	9	76	4900	0	11315	E	25.6297
173200	6	21	5424	6	4461	G	38.82538
323650	11	24	11834	8	9000	G	35.96111
162500	5	19	5246	5	3828	G	42.45037
353500	20	62	11223	2	13680	F	25.84064
134400	4	70	5834	0	4680	E	28.71795
187000	8	19	9075	0	7392	G	25.29762
155700	4	57	5280	0	6030	E	25.8209
93600	4	82	6864	0	3840	F	24.375
110000	4	50	4510	0	3092	G	35.57568
573200	14	10	11192	0	23704	E	24.18157
79300	4	82	7425	0	3876	F	20.45924
272000	5	82	7500	0	9542	E	28.50555

b. (2 points) What single continuous (numeric) variable would you choose to best predict a building's sale price using a straight line? Why? Construct this linear model and provide the equation for it using words and numerical coefficients. c. (3 points) The researchers in this study forgot to add a building to the sample, so they want to use the model you have just built in part (b) to estimate this omitted building's sale price. The omitted building has a value of the independent variable you chose in part (b) equal to 3,100. wHAT IS an 85% prediction interval for the expected sale price of this omitted building. d. (2 points) Your analyst wishes to improve the "fit" of the model you created in part (b) by adding another input variable to the model. He suggests using either "apartments" or "lot size." Decide which of these two additional variables makes more sense to add to the model from part (b). Explain why you made this choice. (3 points) How much of an improvement in explained variability in rating did you gain by adding the variable you chose in part (d) when compared to your earlier, single-input model? Do you have any concerns about this increase in explained variance? f. (2 points) Is the model you created in part (e) significant? Why or why not? Explain using statistics from the regression output. g. (3 points) Now assume that the omitted building from part (c) has 4,300 of the variable you added in part (d). What is the 85% prediction interval for the estimated list price of this building, now? Use the same 3,100 input for the first input variable like you did in part (c). h. (2 points) Which variable has a larger numerical impact on apartment sale pricethe variable from part (b) or the one you added in part (d)?i. (3 points) Allowing for a 10% Type I error tolerance, what is the smallest influence that a unit change in the variable from part (d) would have on the predicted average sale price of an apartment building (assuming that the variable established in part (b) remains unchanged)?j. (2 points) If you are only allowed to build linear models with input variable significance at the 99% level, which variable(s), if any, would you have to remove from the two-variable model you have built thus far?