Exercise 1: Correlation and Linear Regression

For the following exercise, characterize the relationship of the variables and interpret the F-test for the regression model. Using the p-value approach, determine whether the null hypothesis for the F-test is rejected or not. Discuss why or why not. Interpret the implication of these findings for the model.

• (a) Can you determine any correlation between the independent variables Days (number of days the property is on the market) and the Price (market price in dollars)? Similarly, are the Size (livable square feet of the property) and the Price(market price in dollars) correlated? Use the .05 significance level. State the p-value of the test.
• (b) With thePrice (market price in dollars) as the dependent variable and the Size (livable square feet of the property)of the home as the independent variable, determine the regression equation and interpret the confidence level, the precision, and reliability of the sample. Using the regression model, forecast the future market Price for a home with a livable area of 2,200 square feet. Determine the 95% prediction interval for the market price of a home with a livable area of 2,200 square feet.

Exercise 2: Multiple Regression Analysis

Conduct the following analyses using the Price (market price in dollars) as the dependent variable, determine the regression equation with the Bedrooms (number of bedrooms), Size (livable square feet of the property), Township (area the property is located), and theBaths (number of bathrooms) as independent variables.

• (a) Develop a correlation matrix and discuss which independent variables have strong or weak correlations with the dependent variable. Utilize these results to discuss any issues with problems with the multicollinearity.
• (b) Use Excel to determine the multiple regression equation. Discuss how you selected the variables to include in the equation. Your regression equation should demonstrate a significant relationship. Report and interpret the R-square.
• (c) Using your results fromQuestion (b) evaluate the addition of the variables; Pool (1 = yes, 0 = no), and attached Garage (1 = yes, 0 = no). Report your results and conclusions.
• (d) Develop a histogram of the residuals from the final regression equation developed inQuestion (c). Is it reasonable to conclude that the normality assumption has been met?
• (e) Plot the residuals against the fitted values from the final regression equation developed inQuestion (c). Plot the residuals on the vertical axis and the fitted values on the horizontal axis.
• EXCEL DATA:

SYM-506 North Valley Real Estate Case Study Data Set
record	Agent	Price	Size	Bedrooms	Baths	Pool (yes is 1)	Garage (Yes is 1)	Days	Township	Mortgage type	Years	FICO	Default (Yes is 1)
1	Marty	206424	1820	2	1.5	1	1	33	2	Fixed	2	824	0
2	Rose	346150	3010	3	2	0	0	36	4	Fixed	9	820	0
3	Carter	372360	3210	4	3	0	1	21	2	Fixed	18	819	0
4	Peterson	310622	3330	3	2.5	1	0	26	3	Fixed	17	817	0
5	Carter	496100	4510	6	4.5	0	1	13	4	Fixed	17	816	0
6	Peterson	294086	3440	4	3	1	1	31	4	Fixed	19	813	0
7	Carter	228810	2630	4	2.5	0	1	39	4	Adjustable	10	813	0
8	Isaacs	384420	4470	5	3.5	0	1	26	2	Fixed	6	812	0
9	Peterson	416120	4040	5	3.5	0	1	26	4	Fixed	3	810	0
10	Isaacs	487494	4380	6	4	1	1	32	3	Fixed	6	808	0
11	Rose	448800	5280	6	4	0	1	35	4	Fixed	8	806	1
12	Peterson	388960	4420	4	3	0	1	50	2	Adjustable	9	805	1
13	Marty	335610	2970	3	2.5	0	1	25	3	Adjustable	9	801	1
14	Rose	276000	2300	2	1.5	0	0	34	1	Fixed	20	798	0
15	Rose	346421	2970	4	3	1	1	17	3	Adjustable	10	795	0
16	Isaacs	453913	3660	6	4	1	1	12	3	Fixed	18	792	0
17	Carter	376146	3290	5	3.5	1	1	28	2	Adjustable	9	792	1
18	Peterson	694430	5900	5	3.5	1	1	36	3	Adjustable	10	788	0
19	Rose	251269	2050	3	2	1	1	38	3	Fixed	16	786	0
20	Rose	547596	4920	6	4.5	1	1	37	5	Fixed	2	785	0
21	Marty	214910	1950	2	1.5	1	0	20	4	Fixed	6	784	0
22	Rose	188799	1950	2	1.5	1	0	52	1	Fixed	10	782	0
23	Carter	459950	4680	4	3	1	1	31	4	Fixed	8	781	0
24	Isaacs	264160	2540	3	2.5	0	1	40	1	Fixed	18	780	0
25	Carter	393557	3180	4	3	1	1	54	1	Fixed	20	776	0
26	Isaacs	478675	4660	5	3.5	1	1	26	5	Adjustable	9	773	0
27	Carter	384020	4220	5	3.5	0	1	23	4	Adjustable	9	772	1
28	Marty	313200	3600	4	3	0	1	31	3	Fixed	19	772	0
29	Isaacs	274482	2990	3	2	1	0	37	3	Fixed	5	769	0
30	Marty	167962	1920	2	1.5	1	1	31	5	Fixed	6	769	0
31	Isaacs	175823	1970	2	1.5	1	0	28	5	Adjustable	9	766	1
32	Isaacs	226498	2520	4	3	1	1	28	3	Fixed	8	763	1
33	Carter	316827	3150	4	3	1	1	22	4	Fixed	2	759	1
34	Carter	189984	1550	2	1.5	1	0	22	2	Fixed	17	758	0
35	Marty	366350	3090	3	2	1	1	23	3	Fixed	5	754	1
36	Isaacs	416160	4080	4	3	0	1	25	4	Fixed	12	753	0
37	Isaacs	308000	3500	4	3	0	1	37	2	Fixed	18	752	0
38	Rose	294357	2620	4	3	1	1	15	4	Fixed	10	751	0
39	Carter	337144	2790	4	3	1	1	19	3	Fixed	15	749	0
40	Peterson	299730	2910	3	2	0	0	31	2	Fixed	13	748	0
41	Rose	445740	4370	4	3	0	1	19	3	Fixed	5	746	0
42	Rose	410592	4200	4	3	1	1	27	1	Adjustable	9	741	1
43	Peterson	667732	5570	5	3.5	1	1	29	5	Fixed	4	740	0
44	Rose	523584	5050	6	4	1	1	19	5	Adjustable	10	739	0
45	Marty	336000	3360	3	2	0	0	32	3	Fixed	6	737	0
46	Marty	202598	2270	3	2	1	0	28	1	Fixed	10	737	0
47	Marty	326695	2830	3	2.5	1	0	30	4	Fixed	8	736	0
48	Rose	321320	2770	3	2	0	1	23	4	Fixed	6	736	0
49	Isaacs	246820	2870	4	3	0	1	27	5	Fixed	13	735	0
50	Isaacs	546084	5910	6	4	1	1	35	5	Adjustable	10	731	0
51	Isaacs	793084	6800	8	5.5	1	1	27	4	Fixed	6	729	0
52	Isaacs	174528	1600	2	1.5	1	0	39	2	Fixed	15	728	0
53	Peterson	392554	3970	4	3	1	1	30	4	Fixed	17	726	0
54	Peterson	263160	3060	3	2	0	1	26	3	Fixed	10	726	0
55	Rose	237120	1900	2	1.5	1	0	14	3	Fixed	18	723	0
56	Carter	225750	2150	2	1.5	1	1	27	2	Fixed	15	715	0
57	Isaacs	848420	7190	6	4	0	1	49	1	Fixed	5	710	0
58	Carter	371956	3110	5	3.5	1	1	29	5	Fixed	8	710	0
59	Carter	404538	3290	5	3.5	1	1	24	2	Fixed	14	707	0
60	Rose	250090	2810	4	3	0	1	18	5	Fixed	11	704	0
61	Peterson	369978	3830	4	2.5	1	1	27	4	Fixed	10	703	0
62	Peterson	209292	1630	2	1.5	1	0	18	3	Fixed	10	701	0
63	Isaacs	190032	1850	2	1.5	1	1	30	4	Adjustable	2	675	0
64	Isaacs	216720	2520	3	2.5	0	0	2	4	Adjustable	5	674	1
65	Marty	323417	3220	4	3	1	1	22	4	Adjustable	2	673	0
66	Isaacs	316210	3070	3	2	0	0	30	1	Adjustable	1	673	0
67	Peterson	226054	2090	2	1.5	1	1	28	1	Adjustable	6	670	0
68	Marty	183920	2090	3	2	0	0	30	2	Adjustable	8	669	1
69	Rose	248400	2300	3	2.5	1	1	50	2	Adjustable	4	667	0
70	Isaacs	466560	5760	5	3.5	0	1	42	4	Adjustable	3	665	0
71	Rose	667212	6110	6	4	1	1	21	3	Adjustable	8	662	1
72	Peterson	362710	4370	4	2.5	0	1	24	1	Adjustable	2	656	0
73	Rose	265440	3160	5	3.5	1	1	22	5	Adjustable	3	653	0
74	Rose	706596	6600	7	5	1	1	40	3	Adjustable	7	652	1
75	Marty	293700	3300	3	2	0	0	14	4	Adjustable	7	647	1
76	Marty	199448	2330	2	1.5	1	1	25	3	Adjustable	5	644	1
77	Carter	369533	4230	4	3	1	1	32	2	Adjustable	2	642	0
78	Marty	230121	2030	2	1.5	1	0	21	2	Adjustable	3	639	0
79	Marty	169000	1690	2	1.5	0	0	20	1	Adjustable	7	639	1
80	Peterson	190291	2040	2	1.5	1	1	31	4	Adjustable	6	631	1
81	Rose	393584	4660	4	3	1	1	34	3	Adjustable	7	630	1
82	Marty	363792	2860	3	2.5	1	1	48	5	Adjustable	3	626	0
83	Carter	360960	3840	6	4.5	0	1	32	2	Adjustable	5	626	1
84	Carter	310877	3180	3	2	1	1	40	1	Adjustable	6	624	1
85	Peterson	919480	7670	8	5.5	1	1	30	4	Adjustable	1	623	0
86	Carter	392904	3400	3	2	1	0	40	2	Adjustable	8	618	1
87	Carter	200928	1840	2	1.5	1	1	36	4	Adjustable	3	618	1
88	Carter	537900	4890	6	4	0	1	23	1	Adjustable	7	614	0
89	Rose	258120	2390	3	2.5	0	1	23	1	Adjustable	6	614	1
90	Carter	558342	6160	6	4	1	1	24	3	Adjustable	7	613	0
91	Marty	302720	3440	4	2.5	0	1	38	3	Adjustable	3	609	1
92	Isaacs	240115	2220	2	1.5	1	0	39	5	Adjustable	1	609	0
93	Carter	793656	6530	7	5	1	1	53	4	Adjustable	3	605	1
94	Peterson	218862	1930	2	1.5	1	0	58	4	Adjustable	1	604	0
95	Peterson	383081	3510	3	2	1	1	27	2	Adjustable	6	601	1
96	Marty	351520	3380	3	2	0	1	35	2	Adjustable	8	599	1
97	Peterson	841491	7030	6	4	1	1	50	4	Adjustable	8	596	1
98	Marty	336300	2850	3	2.5	0	0	28	1	Adjustable	6	595	1
99	Isaacs	312863	3750	6	4	1	1	12	4	Adjustable	2	595	0
100	Carter	275033	3060	3	2	1	1	27	3	Adjustable	3	593	0
101	Peterson	229990	2110	2	1.5	0	0	37	3	Adjustable	6	591	1
102	Isaacs	195257	2130	2	1.5	1	0	11	5	Adjustable	8	591	1
103	Marty	194238	1650	2	1.5	1	1	30	2	Adjustable	7	590	1
104	Peterson	348528	2740	4	3	1	1	27	5	Adjustable	3	584	1
105	Peterson	241920	2240	2	1.5	0	1	34	5	Adjustable	8	583	1