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March 24, 2022

Use the template that i added and the part one project that I added as well this is part two to this project. Note: In the repor

Mathematics / Statistics

Use the template that i added and the part one project that I added as well this is part two to this project.

Note: In the report you prepare for the sales team, the dependent, or response, variable (y) should be the listing price and the independent, or predictor, variable (x) should be the square feet.

Using the Module Three Assignment Template, specifically address the following:

  • S Regression Equation: Provide the regression equation for the line of best fit using the scatterplot from the Module Two assignment.
  • Determine r: Determine r and what it means. (What is the relationship between the variables?)
    • Determine the strength of the correlation (weak, moderate, or strong).
    • Discuss how you determine the direction of the association between the two variables.
      • Is there a positive or negative association?
      • What do you see as the direction of the correlation?
  • Examine the Slope and Intercepts: Examine the slopeb1 and intercept b0
    • Draw conclusions from the slope and intercept in the context of this problem.
      • Does the intercept make sense based on your observation of the line of best fit?
    • Determine the value of the land only.
      Note: You can assume, when the square footage of the house is zero, that the price is the value of just the land. This happens when x=0, which is the y-intercept. Does this value make sense in context?
  • Determine the R-squared Coefficient: Determine the R-squared value.
    • Discuss what R-squared means in the context of this analysis.
  • Conclusions: Reflect on the Relationship: Reflect on the relationship between square feet and sales price by answering the following questions:
    • Is the square footage for homes in your selected region different than for homes overall in the United States?
    • For every 100 square feet, how much does the price go up (i.e., can you use slope to help identify price changes)?
    • What square footage range would the graph be best used for? 
  • attachment

    mat240-docx-8531789.pdf

  • attachment

    MAT240ModuleThreeAssignmentTemplate-SouthernNewHampshireUniversity.docx

  • attachment

    NationalSummaryStatisticsandGraphsRealEstateData.pdf

  • attachment

    MAT240RealEstateDatacopy.xlsx

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

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

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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,

[Note: To complete this template, replace the bracketed text with your own content. Remove this note before you submit your report.]

Housing Price Prediction Model for D.M. Pan Real Estate Company

[Your Name] Southern New Hampshire University

​

Median Housing Price Prediction Model for D.M. Pan National Real Estate Company ​2

Module Two Notes

[Copy and paste any relevant information from your Module Two assignment here to assist you in completing this assignment. This section is not graded and is only provided to help you easily review Module Two assignment information while completing this assignment.] Regression Equation

[Insert the regression equation for the line of best fit using the scatterplot from your

Module Two assignment.]

Determine r

[Determine r and what it means, including determining the strength of the correlation and discussing how you determine the direction of the association between the two variables.]

Examine the Slope and Intercepts

[Draw conclusions from the slope and intercept in the context of this problem and determine the value of only the land.]

R-squared Coefficient

[Explain what R-squared means in the context of this analysis.] Conclusions

[Reflect on the relationship between square feet and sales price by addressing key considerations such as the comparison between your selected region and overall homes in the United States, as well as analyzing how the slope can help identify price changes, how the regression equation can help identify appropriate listing prices, and what square footage ranges the graph would be best used for.]

,

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
West South Central tx n

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