Statistics Report Part 3 - Statistics
Must format answer in attached template. Must use attachments for data. Must use previous attached assignment for reference.
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
Describe the report: Give a brief description of the purpose of your report.
Define the question your report is trying to answer.
Explain when using linear regression is most appropriate.
When using linear regression, what would you expect the scatterplot to look like?
Explain the difference between response and predictor variables in a linear regression to justify the selection of variables.
Data Collection
Sampling the data: Select a random sample of 50 counties.
Identify your response and predictor variables.
Scatterplot: Create a scatterplot of your response and predictor variables to ensure they are appropriate for developing a linear model.
Data Analysis
Histogram: For your two variables, create histograms.
Summary statistics: For your two variables, create a table to show the mean, median, and standard deviation.
Interpret the graphs and statistics:
Based on your graphs and sample statistics, interpret the center, spread, shape, and any unusual characteristic (outliers, gaps, etc.) for the two variables.
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
Scatterplot: Provide a graph of the scatterplot of the data with a line of best fit.
Explain if a regression model is appropriate to develop based on your scatterplot.
Discuss associations: Based on the scatterplot, discuss the association (direction, strength, form) in the context of your model.
Identify any possible outliers or influential points and discuss their effect on the correlation.
Discuss keeping or removing outlier data points and what impact your decision would have on your model.
Find r: Find the correlation coefficient (r).
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.
Regression equation: Write the regression equation (i.e., line of best fit) and clearly define your variables.
Interpret regression equation: Interpret the slope and intercept in context.
Strength of the equation: Provide and interpret R-squared.
Determine the strength of the linear regression equation you developed.
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
Summarize findings: In one paragraph, summarize your findings in clear and concise plain language for the CEO to understand. Summarize your results.
Did you see the results you expected, or was anything different from your expectations or experiences?
What changes could support different results, or help to solve a different problem?
Provide at least one question that would be interesting for follow-up research.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.]Summary statistics:
Column n Mean Std. dev. Min Q1 Median Q3 Max
median listing price 978 288,407 163,986 75,309 186,742 256,936 337,342 1,653,763
median $s per square
foot
978 142 92 21 95 121 157 1,084
median square feet 978 1,944 367 697 1,726 1,901 2,126 3,945
This graph shows the frequency for median listing price in thousands.
The graph shows the frequency of median square feet.project 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 2Median Housing Price Prediction Model for D.M. Pan National Real Estate Company 2
PREVIOUS ASSIGNMENT TO BE USED FOR REFERENCE
Median Housing Price Prediction Model for D.M. Pan Real Estate Company
NAME
Southern New Hampshire University
Median Housing Price Prediction Model for D.M. Pan Real Estate Company 1
Module Two Notes
Random sample of 30 from the Mountain region.
Mean
Median
Standard deviation
Median Square Feet
2193
2104
380.90
Median Listing Price
$367,828
$321,639
134739
The predictor variable is the median square feet and the response variable is the median listing price.
The regression equation on this graph is Y = 74.683X + 204027
Regression Equation
The regression equation on this graph is Y = 204027 + 74.683X.
(median listing price) Y = 204027 + 74.638X (median sq feet).
Determine r
The meaning of r is to show the strength of the correlation between two variables.
R2 = 0.0446 so r = 0.211187.
Zybooks (2019) shows a table explaining how to determine strength of correlation below.
Based on the fact that r = 0.211187, the strength of the correlation is weak. r is positive, so the direction between the variables is positive.
Examine the Slope and Intercepts
The slope is 204027. The intercept is 74.683X. Based on the slope, land is worth $204,027.
R-squared Coefficient
The purpose of R-squared is to tell you what percentage of data is closest to the regression line. Using R-squared is helpful because you can determine how accurate the regression line is to predicting the value of the response variable. In this particular analysis, R-squared = 0.0446. This means that only 4.46\% of the data I used is closest to the regression line and fits the model. So, the rest of the data, 95.54\%, is farther from the regression line. R-squared explains that the regression line is not very useful in this analysis.
Conclusions
In conclusion, the lower the square feet the lower the listing price will be. However, because only 4\% of my data is closest to the regression line I would recommend the sales team at D.M. Pan Real Estate Company consider some other variables that can have a significant effect on selling prices. I recommend considering variables like quality of the neighborhood, for example, which would factor in nearby schools or walkability to grocery stores and malls. The graph best for this kind of analysis is a box plot because it depicts a much clearer image of the medians.
References
ZyBooks. (2016). MAT 240: Applied Statistics. Zyante. ISBN: 978-1-394-04892-2
Median Square Feet and Median Listing Price
Listing Price
1792.375 1943.8511904999998 1765.4523808333333 2026.9821429166666 2216.0773810000001 2575.8035713333334 2687.3809523333334 1679.6666666666667 1765.3154761666665 2445.1726190833333 2092.4821428333335 2953.3452380833332 2505.7083332500001 2024.0476190833335 2011.3690476666668 2241.7142856666665 2173.2857143333335 2301.5476189999999 1944.36309525 1797.71
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