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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