MAT240.docx 3/19/22, 6:05 AM

Selling Price and Area Analysis for D.M. Pan National Real Estate Company ​1

Report: Selling Price and Area Analysis for D.M. Pan National Real Estate Company

[Your Name]

Southern New Hampshire University ​ Median Housing Price Prediction Model for D. M. Pan National Real Estate Company ​9

Introduction D. M. Pan National Real Estate Company's CEO aims to assist their real estate agents in estimating home prices based on square feet. As a junior data analyst employee, I've been asked to write a research on how square footage influences housing values in the country. According to studies, the square footage of a home is closely proportional to its price. As a result, the bigger the square footage, the more expensive the residence. This report uses data from all house prices in the United States in 2019 to create a regression model that predicts home prices using square footage, with the goal of proving if the hypothesis is correct. Because the variables in the frequency plots from the National Statistics and Graph Document are normally distributed, linear regression is acceptable for this study. The x and y variables are also included in the variables. The square footage is the independent or predictor variable, while the home listing prices are the dependent or predicted variable, represented by the y variable. The scatter plot should show a rising trend to the right, showing a positive relationship. The response variable is a dependent variable which is influenced by the predictor variable, whereas the predictor variable is an independent variable which is unaffected by other variables. The predictor variable in this scenario is square footage while the responder variable is listing prices, which are influenced by square footage.

Data Collection From a total population of 1000 households, a sample of 50 homes was chosen to be analyzed in the research. The sample was chosen using a simple random sampling in which 20 residences were chosen from the population's data received from the 2019 Real Estate County statistics. The study's key variables are the listing price which is the dependent variable and square feet which is the independent variable. Figure 1 depicts a scatter plot of home listing prices vs square footage in sample populations of homes sold in the United States in 2019. Figure 1.

Data Analysis

The histograms in Figures 1 and 2 are based on sample data of listing prices and square feet, respectively. Figure 2.

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Figure 3.

The summary statistics for both the square feet and listing prices variables are shown in Table 1 below. Table 1. square feet listing price Mean 2566.92 342574 Standard Error 211.5122 16572.59 Median 1977 333250 Mode 5284 265400 Standard Deviation 1495.617 117185.9 Sample Variance 2236871 1.37E+10 Kurtosis 0.714474 3.96408 Skewness 1.471359 1.713201 Range 5275 575800 Minimum 1145 169700 Maximum 6420 745500 Sum 128346 17128700 Count 50 50

The sigma curve form of the histogram on the sample data of listing prices is somewhat skewed to the left. Its shape is similar to the median listing price frequency table in the National statistics graphs article. The means of the population and sample data, however, diverge, as seen in the summary statistics tables. The histogram also indicates a gap between 609700 and 719700, indicating that the listing prices in that range were either absent or relatively low. The listed prices ranged from 169,700 to 745,500 dollars. The histogram for square feet illustrates that the majority of the often occurring square feet in the sample are on the right side of the graph, with the number of square feet decreasing as the number of square feet increases. As shown in the National statistics graphics paper, the histogram's shape differs from that of the population. The population data exhibits a normal distribution with a perfect sigma curve. There is a gap between 2545 and 3945 square feet, according to the sample statistics histogram. Since the sample mean is 2566.92 and the population mean is 1944, there is also a disparity between the sample mean and the population mean.

The Regression Model

Scatter plot of square feet versus listing prices containing the trend line, r-square and regression equation is shown in figure 4. Figure 4.

Figure 4 demonstrates that the majority of the data points do not deviate from the trend line, and the trend line rises to the right. The data pattern indicates that the dependent variable, may be projected, and hence a regression model for prediction can be created. This can be done by forming the equation using the trend line or by running a regression analysis. The scatter plot reveals a substantial positive relationship between home square feet and listing prices. The positive correlation indicates that when the square footage of a home increases, so does the listing price, indicating that the variables are directly proportionate. The trend line's angle indicates the strength of the relationship and that the majority of data points lie around the line of best feet. The output summary of the regression analysis for the two variables is shown in Table 2.

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Table 2. Regression Statistics Multiple R 0.904239 R Square 0.817648 Adjusted R Square 0.813849 Standard Error 81024.21 Observations 50

The variables exhibit a high positive connection with an r-value of 0.904. This backs up the scatter plot's visualization conclusions that there is a large positive association between listing prices and the sample's square footage.

The Line of Best Fit The regression equation to be used in this study is derived from table 3 below. This is because the table contains the coefficients and the constant. Table 3.

Coefficients Standard

Error t Stat P-value Intercept 102058.7 22933.67 4.450168 5.09E-05 square feet 113.5389 7.739204 14.67062 2.31E-19

Therefore, the regression equation derived is in the form;

Y = 113.5389X + 102058.7 Where X = Square feet

Y = Listing price The slope is 113.5389. The Y-intercept, where the line of best fit crosses the Y axis, is 10258.7. The independent variable square feet explains 81.78 percent of total differences in listing price variables, according to R-squared of 0.8178. By substituting the value of square feet in X, the regression equation may forecast the listing price of a home using square feet. Using a square foot of 7000 as an example, we may forecast the following listing price:

Y = 113.5389(7000) + 102058.7 Y = 794772.3 + 102058.7

Y = 896831 As a result, when the square foot is 7000, the listing price is expected to be 8996831.

Conclusions According to this study, square footage is directly proportional to property listing prices in the United States. The histogram of square feet produced unexpected results, as it was expected to be closer to normal than the population's frequency table. However, because of a strong positive correlation of 0.9042, which is extremely close to 1, it has a significant impact on a home's listing price. The study raises the intriguing question of whether there are other characteristics that influence property listing prices and whether they may be utilized to anticipate them.

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Summary Statistics for MAT 240 Real Estate Data (for dataset in Modules 2, 3, and 4)

n Mean Median Std. Dev. Min Q1 Q3 Max

Listing

price ($)

1,000 342,365 318,000 125,914 135,300 265,250 381,600 987,600

Cost per

square

foot ($)

1,000 169 166 41 71 139 191 344

Square

feet

1,000 2,111 1,881 921 1,101 1,626 2,215 6,516

This graph shows the frequency for listing price.

This graph shows the frequency for square feet.

project 1 data

Real Estate County Data for 2019
2019 Data (n=1000)
Region	State	County	listing price	$'s per square foot	square feet
East North Central	in	grant	219,500	$116	1,898
East North Central	il	vermilion	254,500	$156	1,632
East North Central	in	henry	235,000	$148	1,588
East North Central	in	wayne	203,800	$141	1,441
East North Central	il	coles	220,800	$117	1,893
East North Central	il	macoupin	197,600	$111	1,783
East North Central	in	vigo	165,800	$122	1,362
East North Central	oh	jefferson	246,500	$136	1,814
East North Central	il	jackson	154,300	$105	1,463
East North Central	oh	marion	149,700	$116	1,296
East North Central	mi	bay	145,100	$117	1,239
East North Central	il	whiteside	283,700	$136	2,087
East North Central	oh	trumbull	243,000	$133	1,827
East North Central	in	madison	229,100	$187	1,224
East North Central	il	knox	205,100	$118	1,740
East North Central	il	stephenson	235,600	$140	1,682
East North Central	il	macon	212,900	$128	1,659
East North Central	in	delaware	221,600	$134	1,651
East North Central	il	henry	257,700	$123	2,087
East North Central	oh	seneca	211,900	$168	1,263
East North Central	oh	darke	160,800	$114	1,416
East North Central	oh	scioto	204,200	$131	1,562
East North Central	oh	belmont	172,500	$101	1,710
East North Central	oh	sandusky	253,900	$146	1,738
East North Central	il	rock island	166,300	$127	1,305
East North Central	oh	clark	240,500	$137	1,752
East North Central	oh	columbiana	241,400	$164	1,469
East North Central	in	howard	304,300	$152	1,996
East North Central	oh	richland	248,900	$132	1,880
East North Central	il	peoria	187,900	$131	1,434
East North Central	il	la salle	311,100	$154	2,015
East North Central	il	madison	254,500	$156	1,628
East North Central	mi	wayne	213,800	$172	1,243
East North Central	in	vanderburgh	214,100	$134	1,596
East North Central	oh	mahoning	207,500	$123	1,688
East North Central	il	williamson	171,600	$141	1,218
East North Central	il	winnebago	236,700	$140	1,692
East North Central	il	adams	266,100	$166	1,599
East North Central	mi	saginaw	171,800	$118	1,452
East North Central	oh	montgomery	225,300	$151	1,493
East North Central	oh	allen	227,600	$147	1,550
East North Central	oh	lucas	228,300	$115	1,978
East North Central	oh	ashtabula	177,000	$107	1,658
East North Central	oh	lawrence	248,300	$156	1,587
East North Central	oh	huron	199,700	$147	1,359
East North Central	il	tazewell	278,700	$165	1,693
East North Central	oh	summit	185,800	$101	1,847
East North Central	il	sangamon	213,500	$130	1,643
East North Central	oh	ashland	188,000	$151	1,246
East North Central	oh	tuscarawas	270,700	$149	1,815
East North Central	oh	ross	257,200	$127	2,018
East North Central	mi	shiawassee	192,400	$129	1,494
East North Central	mi	calhoun	266,200	$130	2,042
East North Central	il	kankakee	148,700	$115	1,293
East North Central	in	lawrence	270,600	$137	1,978
East North Central	wi	manitowoc	181,400	$140	1,294
East North Central	il	st. clair	201,400	$164	1,225
East North Central	mi	ingham	222,500	$125	1,777
East North Central	il	mclean	203,800	$134	1,526
East North Central	mi	jackson	139,200	$116	1,201
East North Central	mi	isabella	163,000	$125	1,307
East North Central	wi	wood	266,500	$144	1,853
East North Central	mi	montcalm	218,300	$105	2,081
East North Central	wi	grant	243,200	$121	2,014
East North Central	oh	cuyahoga	265,100	$136	1,947
East North Central	oh	stark	201,000	$163	1,230
East North Central	oh	athens	246,400	$158	1,560
East North Central	wi	milwaukee	184,900	$111	1,666
East North Central	mi	lenawee	191,500	$118	1,628
East North Central	wi	fond du lac	135,300	$103	1,312
East North Central	in	st. joseph	193,000	$111	1,736
East North Central	mi	ionia	193,600	$137	1,416
East North Central	mi	genesee	194,800	$166	1,173
East North Central	oh	muskingum	188,300	$94	1,999
East North Central	il	ogle	236,600	$208	1,138
East North Central	oh	washington	324,400	$156	2,081
East North Central	oh	wayne	256,700	$129	1,986
East North Central	mi	muskegon	230,400	$131	1,757
East North Central	oh	pickaway	265,700	$143	1,853
East North Central	mi	st. joseph	188,500	$135	1,397
East North Central	il	champaign	246,700	$121	2,031
East North Central	oh	knox	192,200	$127	1,510
East North Central	oh	lorain	226,200	$126	1,789
East North Central	wi	calumet	226,400	$111	2,033
East North Central	mi	midland	174,500	$151	1,157
East North Central	mi	marquette	172,500	$120	1,433
East North Central	in	elkhart	202,300	$182	1,113
East North Central	mi	monroe	228,600	$136	1,679
East North Central	oh	lake	225,900	$135	1,676
East North Central	mi	eaton	189,900	$96	1,976
East North Central	wi	douglas	461,400	$129	3,581
East North Central	wi	marathon	431,200	$119	3,638
East North Central	il	dekalb	347,500	$97	3,574
East North Central	in	marion	323,300	$95	3,408
East North Central	in	allen	398,000	$113	3,525
East North Central	oh	hancock	380,300	$94	4,028
East North Central	in	lake	470,600	$109	4,316
East North Central	wi	portage	531,000	$109	4,888
East North Central	wi	rock	513,100	$104	4,950
East North Central	oh	greene	581,800	$113	5,146
West South Central	ar	baxter	286,900	$132	2,176
West South Central	ar	benton	232,900	$138	1,690
West South Central	ar	craighead	251,100	$110	2,285
West South Central	ar	crawford	172,900	$100	1,734
West South Central	ar	crittenden	298,800	$155	1,928
West South Central	ar	faulkner	280,500	$129	2,168
West South Central	ar	garland	274,800	$134	2,056
West South Central	ar	jefferson	314,600	$144	2,179
West South Central	ar	lonoke	289,000	$132	2,190
West South Central	ar	pope	273,200	$114	2,389
West South Central	ar	pulaski	211,300	$121	1,745
West South Central	ar	saline	273,500	$114	2,396
West South Central	ar	sebastian	208,600	$111	1,879
West South Central	ar	washington	215,600	$126	1,712
West South Central	ar	white	254,800	$145	1,763
West South Central	la	acadia	226,300	$135	1,681
West South Central	la	ascension	303,200	$149	2,030
West South Central	la	bossier	305,500	$140	2,177
West South Central	la	caddo	278,500	$158	1,768
West South Central	la	calcasieu	214,300	$115	1,871
West South Central	la	east baton rouge	254,100	$135	1,881
West South Central	la	iberia	188,700	$125	1,511
West South Central	la	jefferson	306,100	$131	2,344
West South Central	la	lafayette	221,000	$108	2,040
West South Central	la	lafourche	297,000	$128	2,320
West South Central	la	livingston	297,300	$139	2,135
West South Central	la	orleans	258,600	$152	1,698
West South Central	la	ouachita	304,300	$158	1,921
West South Central	la	rapides	347,800	$151	2,297
West South Central	la	st. charles	171,400	$99	1,724
West South Central	la	st. landry	254,700	$118	2,150
West South Central	la	st. martin	252,600	$137	1,845
West South Central	la	st. mary	260,400	$141	1,842
West South Central	la	st. tammany	280,300	$150	1,869
West South Central	la	tangipahoa	242,300	$110	2,202
West South Central	la	terrebonne	254,700	$156	1,637
West South Central	la	vermilion	270,600	$164	1,650
West South Central	la	vernon	255,900	$113	2,256
West South Central	ok	canadian	218,000	$95	2,290
West South Central	ok	carter	263,000	$142	1,856
West South Central	ok	cherokee	302,100	$167	1,809
West South Central	ok	cleveland	263,800	$117	2,262
West South Central	ok	comanche	252,100	$140	1,806
West South Central	ok	creek	362,200	$157	2,305
West South Central	ok	garfield	220,300	$132	1,670
West South Central	ok	grady	229,500	$158	1,455
West South Central	ok	le flore	292,200	$128	2,291
West South Central	ok	muskogee	206,400	$125	1,646
West South Central	ok	oklahoma	219,000	$121	1,804
West South Central	ok	osage	194,800	$129	1,515
West South Central	ok	payne	272,200	$124	2,204
West South Central	ok	pottawatomie	204,800	$136	1,510
West South Central	ok	rogers	183,700	$104	1,769
West South Central	ok	tulsa	295,000	$130	2,267
West South Central	ok	wagoner	209,100	$134	1,560
West South Central	ok	washington	167,100	$110	1,526
West South Central	tx	angelina	270,200	$172	1,568
West South Central	tx	bastrop	179,600	$103	1,736
West South Central	tx	bell	323,100	$143	2,262
West South Central	tx	bexar	260,800	$111	2,359
West South Central	tx	bowie	223,600	$153	1,463
West South Central	tx	brazoria	246,300	$130	1,900
West South Central	tx	brazos	242,500	$132	1,835
West South Central	tx	cameron	269,200	$151	1,781
West South Central	tx	collin	374,700	$161	2,325
West South Central	tx	comal	249,200	$165	1,510
West South Central	tx	coryell	184,100	$126	1,460
West South Central	tx	dallas	279,600	$144	1,940
West South Central	tx	denton	254,500	$124	2,052
West South Central	tx	ector	151,300	$102	1,477
West South Central	tx	el paso	249,200	$123	2,023
West South Central	tx	ellis	163,400	$112	1,459
West South Central	tx	fort bend	222,800	$114	1,958
West South Central	tx	galveston	296,100	$139	2,127
West South Central	tx	grayson	248,700	$135	1,837
West South Central	tx	gregg	188,200	$112	1,679
West South Central	tx	guadalupe	263,800	$146	1,804
West South Central	tx	hardin	283,500	$152	1,867
West South Central	tx	harris	196,200	$115	1,700
West South Central	tx	harrison	255,300	$107	2,396
West South Central	tx	hays	230,000	$154	1,490
West South Central	tx	henderson	285,700	$122	2,343
West South Central	tx	hidalgo	224,600	$121	1,853
West South Central	tx	hood	207,200	$91	2,278
West South Central	tx	hunt	306,900	$133	2,299
West South Central	tx	jefferson	213,500	$99	2,154
West South Central	tx	johnson	234,900	$115	2,040
West South Central	tx	kaufman	264,300	$134	1,977
West South Central	tx	kerr	262,900	$139	1,888
West South Central	tx	liberty	206,400	$113	1,822
West South Central	tx	lubbock	476,700	$133	3,583
West South Central	tx	mclennan	407,300	$104	3,920
West South Central	tx	midland	515,000	$141	3,648
West South Central	tx	montgomery	480,300	$116	4,142
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