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 the Price (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 the Baths (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 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

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Question: 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

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 thep-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 variablesDays (number of days the property is on the market)and thePrice (market price in dollars)? Similarly, are theSize (livable square feet of the property)and thePrice(market price in dollars)correlated? Use the .05 significance level. State thep-value of the test.

(b) With thePrice (market price in dollars)as the dependent variable and theSize (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 marketPricefor 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 thePrice (market price in dollars)as the dependent variable, determine the regression equation with theBedrooms (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 attachedGarage (1 = yes, 0 = no).Report your results and conclusions.

(d) Develop a histogram of the residuals from thefinal regressionequation developed inQuestion (c). Is it reasonable to conclude that the normality assumption has been met?

(e) Plot the residuals against the fitted values from thefinal regressionequation developed inQuestion (c). Plot the residuals on the vertical axis and the fitted values on the horizontal axis.

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

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