4-3 Project One Submission - Statistics
Competencies
In this project, you will demonstrate your mastery of the following competencies:
Apply statistical techniques to address research problems
Perform regression analysis to address an authentic problem
Overview
The purpose of this project is to have you complete all of the steps of a real-world linear regression research project starting with developing a research question, then completing a comprehensive statistical analysis, and ending with summarizing your research conclusions.
Scenario
You have been hired by the D. M. Pan National Real Estate Company to develop a model to predict median housing prices for homes sold in 2019. The CEO of D. M. Pan wants to use this information to help their real estate agents better determine the use of square footage as a benchmark for listing prices on homes. Your task is to provide a report predicting the median housing prices based square footage. To complete this task, use the provided real estate data set for all U.S. home sales as well as national descriptive statistics and graphs provided.
Directions
Using the Project One Template located in the What to Submit section, generate a report including your tables and graphs to determine if the square footage of a house is a good indicator for what the listing price should be. Reference the National Statistics and Graphs document for national comparisons and the Real Estate County Data spreadsheet (both found in the Supporting Materials section) for your statistical analysis.
Note: Present your data in a clearly labeled table and using clearly labeled graphs.
Specifically, include the following in your report:
Introduction
A. Describe the report: Give a brief description of the purpose of your report.
a. Define the question your report is trying to answer.
b. Explain when using linear regression is most appropriate.
i. When using linear regression, what would you expect the scatterplot to look like?
c. Explain the difference between response and predictor variables in a linear regression to justify the selection of variables.
Data Collection
A. Sampling the data: Select a random sample of 50 counties.
a. Identify your response and predictor variables.
B. Scatterplot: Create a scatterplot of your response and predictor variables to ensure they are appropriate for developing a linear model.
Data Analysis
A. Histogram: For your two variables, create histograms.
B. Summary statistics: For your two variables, create a table to show the mean, median, and standard deviation.
C. Interpret the graphs and statistics:
a. Based on your graphs and sample statistics, interpret the center, spread, shape, and any unusual characteristic (outliers, gaps, etc.) for the two variables.
b. Compare and contrast the shape, center, spread, and any unusual characteristic for your sample of house sales with the national population. Is your sample representative of national housing market sales?
Develop Your Regression Model
A. Scatterplot: Provide a graph of the scatterplot of the data with a line of best fit.
a. Explain if a regression model is appropriate to develop based on your scatterplot.
B. Discuss associations: Based on the scatterplot, discuss the association (direction, strength, form) in the context of your model.
b. Identify any possible outliers or influential points and discuss their effect on the correlation.
c. Discuss keeping or removing outlier data points and what impact your decision would have on your model.
C. Find r: Find the correlation coefficient (r).
b. Explain how the r value you calculated supports what you noticed in your scatterplot.
Determine the Line of Best Fit. Clearly define your variables. Find and interpret the regression equation. Assess the strength of the model.
A. Regression equation: Write the regression equation (i.e., line of best fit) and clearly define your variables.
B. Interpret regression equation: Interpret the slope and intercept in context.
C. Strength of the equation: Provide and interpret R-squared.
a. Determine the strength of the linear regression equation you developed.
D. Use regression equation to make predictions: Use your regression equation to predict how much you should list your home for based on the square footage of your home.
Conclusions
A. Summarize findings: In one paragraph, summarize your findings in clear and concise plain language for the CEO to understand. Summarize your results.
a. Did you see the results you expected, or was anything different from your expectations or experiences?
i. What changes could support different results, or help to solve a different problem?
ii. Provide at least one question that would be interesting for follow-up research.
What to Submit
To complete this project, you must submit the following:
Project One Template: Use this template to structure your report, and submit the finished version as a Word document.
Supporting Materials
The following resources may help support your work on the project:
Document: National Statistics and Graphs
Use this data for input in your project report.
Spreadsheet: Real Estate County Data
Use this data for input in your project report.
Tutorial: Downloading Office 365 Programs
Use this tutorial for support with Office 365 programs.
Use these tutorials for support with the Excel functions you will use in the project:Median Housing Price Model for D. M. Pan National Real Estate Company 3
[Note: To complete this template, replace the bracketed text with your own content. Remove this note before you submit your outline.]
Report: Median Housing Price Prediction Model for D. M. Pan National Real Estate Company
[Your Name]
Median Housing Price Prediction Model for D. M. Pan National Real Estate Company 1
Southern New Hampshire University
Introduction
[Describe the report: Include in this section a brief overview, including the purpose of the report and your approach.]
Data Collection
[Sampling the data: Outline how you obtained your sample data, including the response and predictor variables.]
[Scatterplot: Insert a correctly labeled scatterplot of your chosen variables.]
Data Analysis
[Describe your study briefly. Discuss the requirements of the data sets for a linear regression. Explain the difference between response and predictor variables in a linear regression to justify the selection of variables.]
[Histogram: Insert the histogram of the two variables. Be sure to include appropriate labels.]
[Summary statistics: Insert a table to show the summary statistics.]
[Interpret the graphs and statistics: Describe the shape, center, spread, and any unusual characteristic (outliers, gaps, etc.) and what they mean based on your sample data and the graphs you created.]
[Explain how these characteristics of the sample data compare to the same characteristics of the national population. Also, determine whether your sample is representative of the national housing market sales.]
The Regression Model
[Scatterplot: Include the scatterplot graph of the sample with a line of best fit.]
[Based on your graph, explain whether a regression model can be developed for the data and how.]
[Discuss associations: Explain the associations in the scatterplot, including the direction, strength, form in the context of your model.]
[Find r: Calculate the correlation coefficient and explain how it aligns with your interpretation of the data from the scatterplot.]
The Line of Best Fit
[Regression equation: Insert the regression equation.]
[Interpret regression equation: Interpret the slope and intercept in context.]
[Strength of the equation: Interpret the strength of the regression equation, R-squared.]
[Use regression equation to make predictions: Use the regression equation to make a sample prediction.]
Conclusions
[Summarize findings: Summarize your findings in clear and concise plain language. Outline any questions arising from the study that might be interesting for follow-up research.]New England
House Listing Price Data by Region Source: https://www.realtor.com/research/data/
Regional sample (n = 1000)
State County Region House listing price Cost per square foot Square footage
CT litchfield New England $329,050 $153 1,888
ME penobscot New England $169,500 $103 1,586
NH merrimack New England $299,950 $145 2,152
VT washington New England $289,950 $141 1,959
ME york New England $391,550 $230 1,719
VT washington New England $222,500 $135 1,670
NH strafford New England $311,471 $166 1,885
MA suffolk New England $699,050 $647 1,259
MA norfolk New England $642,500 $309 2,210
NH hillsborough New England $339,950 $164 2,090
RI washington New England $499,050 $259 1,871
NH belknap New England $289,950 $156 1,869
VT rutland New England $228,800 $117 1,993
RI newport New England $579,050 $292 2,128
MA franklin New England $230,050 $133 1,800
ME penobscot New England $157,050 $94 1,600
VT washington New England $300,050 $154 1,896
MA berkshire New England $379,950 $185 2,032
ME kennebec New England $187,050 $104 1,695
NH cheshire New England $266,550 $132 1,981
VT franklin New England $219,950 $120 1,750
CT new london New England $290,000 $153 1,848
NH merrimack New England $314,950 $146 2,174
NH merrimack New England $299,950 $140 2,176
NH hillsborough New England $358,950 $173 2,036
CT windham New England $204,000 $123 1,615
VT washington New England $295,050 $147 1,888
CT new london New England $268,500 $159 1,648
CT new haven New England $279,950 $158 1,724
MA plymouth New England $491,550 $244 2,028
MA franklin New England $223,800 $135 1,780
NH cheshire New England $260,500 $131 1,838
CT new haven New England $279,050 $153 1,790
ME penobscot New England $159,750 $100 1,588
NH grafton New England $259,300 $150 1,840
VT washington New England $299,050 $147 1,850
ME york New England $339,050 $205 1,772
CT new haven New England $272,421 $150 1,763
MA suffolk New England $764,050 $669 1,341
NH grafton New England $253,850 $143 1,741
RI newport New England $598,050 $292 2,170
MA middlesex New England $655,000 $276 2,400
MA franklin New England $299,050 $150 1,960
CT new london New England $274,950 $121 1,212
RI providence New England $279,050 $185 1,504
MA barnstable New England $599,950 $318 1,920
CT litchfield New England $398,050 $172 2,268
NH belknap New England $295,000 $162 1,838
NH belknap New England $269,950 $153 1,797
MA suffolk New England $799,050 $708 1,311
RI kent New England $275,050 $177 1,524
CT new haven New England $258,500 $146 1,410
VT windsor New England $349,050 $158 2,120
CT litchfield New England $329,950 $150 1,776
NH cheshire New England $234,550 $123 1,845
NH cheshire New England $258,864 $126 1,968
NH hillsborough New England $341,444 $160 2,126
RI washington New England $489,950 $253 1,812
CT middlesex New England $342,450 $170 1,874
CT new london New England $294,050 $154 1,8project 1 data
Real Estate County Data for 2019 Source: https://www.realtor.com/research/data/
2019 County Data (n=978) Excel Filename created: RDC_Inventory_Core_Metrics_County_History.csv
County level measures are based on averages
Region State County median listing price median $s per square foot median square feet
East North Central il adams $135,215 $88 1598
East North Central il champaign $191,054 $107 1760
East North Central il coles $93,141 $65 1591
East North Central il cook $314,629 $166 1442
East North Central il dekalb $210,494 $108 1844
East North Central il dupage $412,547 $181 2203
East North Central il grundy $254,322 $118 1936
East North Central il henry $110,053 $69 1449
East North Central il jackson $99,574 $64 1620
East North Central il kane $321,961 $136 2329
East North Central il kankakee $151,231 $96 1577
East North Central il kendall $266,967 $119 2140
East North Central il knox $106,418 $67 1590
East North Central il la salle $127,516 $84 1482
East North Central il lake $408,310 $159 2529
East North Central il macon $106,893 $61 1749
East North Central il macoupin $94,494 $64 1494
East North Central il madison $128,071 $82 1591
East North Central il mchenry $279,481 $124 2173
East North Central il mclean $157,728 $89 1780
East North Central il ogle $178,639 $90 1867
East North Central il peoria $127,413 $71 1811
East North Central il rock island $121,610 $88 1440
East North Central il sangamon $145,027 $81 1781
East North Central il st. clair $156,788 $82 1767
East North Central il stephenson $106,561 $60 1704
East North Central il tazewell $138,981 $78 1803
East North Central il vermilion $78,821 $54 1577
East North Central il whiteside $103,858 $71 1457
East North Central il will $289,846 $132 2181
East North Central il williamson $130,832 $76 1651
East North Central il winnebago $133,320 $76 1676
East North Central in allen $212,572 $98 1927
East North Central in bartholomew $280,054 $101 2712
East North Central in boone $448,568 $118 3700
East North Central in clark $249,307 $121 1876
East North Central in dearborn $220,555 $95 1778
East North Central in delaware $107,724 $69 1540
East North Central in elkhart $198,174 $92 2117
East North Central in floyd $232,319 $105 2098
East North Central in grant $75,309 $53 1510
East North Central in hamilton $378,444 $115 3483
East North Central in hancock $322,137 $106 3098
East North Central in hendricks $290,093 $108 2662
East North Central in henry $83,253 $57 1545
East North Central in howard $124,139 $77 1571
East North Central in johnson $274,236 $106 2641
East North Central in kosciusko $252,047 $131 1864
East North Central in la porte $251,713 $114 1898
East North Central in lake $215,915 $111 1902
East North Central in lawrence $155,672 $87 1745
East North Central in madison $105,965 $63 1709
East North Central in marion $210,745 $96 2
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