The owner of an apartment building in Minneapolis believed that her property tax bill was too high because of an overassessment of the property's value by the city tax assessor. The owner hired an independent real estate appraiser to investigate the appropriateness of the city's assessment. The appraiser used regression analysis to explore the relationship between the sale prices of apartment buildings sold in Minneapolis and various characteristics of the properties. Twenty-five apartment buildings were randomly sampled from all apartment buildings that were sold during a recent year. The following table lists the data collected by the appraiser. The real estate appraiser hypothesized that the sale price (that is, market value) of an apartment building is related to the other variables in the table according to the model

y = ₀ + ₁x₁ + ₂x₂ + ₃x₃ + ₄x₄ + ₅x₅ +.

Code No.	Sale Price, y ($)	No. of Apartments, x1	Age of Structure, x2 (years)	Lot Size, x3 (sq. ft)	No. of On-Site Parking Spaces, x4	Gross Building Area, x5(sq.ft)
0229	90,300	4	82	4,635	0	4,266
0094	384,000	20	13	17,798	0	14,391
0043	157,500	5	66	5,913	0	6,615
0079	676,200	26	64	7,750	6	34,144
0134	165,000	5	55	5,150	0	6,120
0179	300,000	10	65	12,506	0	14,552
0087	108,750	4	82	7,160	0	3,040
0120	276,538	11	23	5,120	0	7,881
0246	420,000	20	18	11,745	20	12,600
0025	950,000	62	71	21,000	3	39,448
0015	560,000	26	74	11,221	0	30,000
0131	268,000	13	56	7,818	13	8,088
0172	290,000	9	76	4,900	0	11,315
0095	173,200	6	21	5,424	6	4,461
0121	323,650	11	24	11,834	8	9,000
0077	162,500	5	19	5,246	5	3,828
0060	353,500	20	62	11,223	2	13,680
0174	134,400	4	70	5,834	0	4,680
0084	187,000	8	19	9,075	0	7,392

Table continued

Code No.	Sale Price, y ($)	No. of Apartments, x1	Age of Structure, x2 (years)	Lot Size, x3 (sq. ft)	No. of On-Site Parking Spaces, x4	Gross Building Area, x5(sq.ft)
0031	155,700	4	57	5,280	0	6,030
0019	93,600	4	82	6,864	0	3,840
0074	110,000	4	50	4,510	0	3,092
0057	573,200	14	10	11,192	0	23,704
0104	79,300	4	82	7,425	0	3,876
0024	272,000	5	82	7,500	0	9,542

1. Fit the real estate appraiser's model to the data in the table. Report the least squares prediction equation.
2. Find the standard deviation of the regression model and interpret its value in the context of this problem.
3. Do the data provide sufficient evidence to conclude that value increases with the number of units in an apartment building? Report the observed significance level and reach a conclusion using =0.05