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 calculate 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 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 housing prices based square footage. 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 theReal Estate Dataspreadsheet (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

1. Describe the report:Give a brief description of the purpose of your report.
2. Define the question your report is trying to answer.
3. Explain when using linear regression is most appropriate.
4. When using linear regression, what would you expect the scatterplot to look like?
5. Explain the difference between response and predictor variables in a linear regression to justify the selection of variables.

Data Collection

1. Sampling the data:Select a random sample of 50 houses.
2. Identify your response and predictor variables.
3. Scatterplot:make a scatterplot of your response and predictor variables to ensure they are appropriate for developing a linear model.

Data Analysis

1. Histogram:For your two variables, create histograms.
2. Summary statistics:For your two variables, make a table to show the mean, median, and standard deviation.
3. Interpret the graphs and statistics:
4. Based on your graphs and sample statistics, interpret the center, spread, shape, and any unusual characteristic (outliers, gaps, etc.) for the two variables.
5. 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

1. Scatterplot:Provide a graph of the scatterplot of the data with a line of best fit.
2. Explain if a regression model is appropriate to develop based on your scatterplot.
3. Discuss associations:Based on the scatterplot, discuss the association (direction, strength, form) in the context of your model.
4. Identify any possible outliers or influential points and discuss their effect on the correlation.
5. Discuss keeping or removing outlier data points and what impact your decision would have on your model.
6. Findr:Find the correlation coefficient (r).
7. Explain how thervalue 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.

1. Regression equation:Write the regression equation (i.e., line of best fit) and clearly define your variables.
2. Interpret regression equation:Interpret the slope and intercept in context.
3. Strength of the equation:Provide and interpretR-squared.
4. Determine the strength of the linear regression equation you developed.
5. 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

1. Summarize findings:In one paragraph, summarize your findings in clear and concise plain language for the CEO to understand. Summarize your results.
2. Did you see the results you expected, or was anything different from your expectations or experiences?
3. What changes could support different results, or help to solve a different problem?
4. Provide at least one question that would be interesting for follow-up research.

DATA:

real estate data

Sur'rlrnar'glI statistics: Column n Mean Std. dew. Min Q1 Median (13 Max median listing price 978 288,407 163,986 75,309 186,?42 256,936 33?,342 1,653,763 median S's per square 978 142 92 21 95 121 15'.Ir 1,084 foot median square feet 978 1.944 367 69? 1,?26 1,901 2,126 3.945 Frequency 400 560 1600 1500 median listing price ($000) This graph shows the frequency for median listing price In thousands. Frequency 150 100 [000 3000 median square feet The graph shows the frequency of median square feet. 2019 Data [n=1000) raluulnyll dl'lm 1.x...\" .5 East North Central oh 93101903 172,500 $101 1,710 East North Central oh 53m 253,900 $146 1,733 5'5 1m Sill-ale Region state County listing prise square foot feet East North Central i| roek island 166,300 $127 1,305 East North Central in grant 219,500 $116 1,393 East North Central oh slant, 240.500 5137 1,752 East North Central il venniion 254,500 $156 1,632 East North Central oh wiumbiana. 241,400 $164 1,469 Eam North Central in henry- 235,000 $143 1,533 East North Central in 0900.901 304,300 $152 1,996 East North Central in 931103 203301) 5141 1,441 East North Central oh 11mm 243,900 $132 1,630 Eam North Central il gates, 220,300 $117 1,393 East North Central H m 137,900 $131 1,434 East North Central 11 m 197,600 5111 1,733 East North Central i| la salle 311,100 $154 2,015 East North Central in 91119 165,300 $12 1,362 East North Central 11 mm 254,500 $156 1,623 East North Central oh 131131399 246,500 $136 1,314 East North Central mi 91.430: 213,300 $172 1,243 East North Central il Mm 154,300 $105 1,463 East Nnh Central in 365313090099 214.100 $134 1,596 Eam North Central oh 016099. 149,700 $116 1,296 East North Central oh mm 207,500 $123 1,633 East North Central mi bay 145,100 $117 1,239 East North Central H mm 171,600 $141 1,213 East North Central il m 233,700 $136 2,037 East North Central i| 300939609, 236.700 $140 1,692 East North Central oh 1510:9101". 243,000 $133 1,327 East North Central H was); 266,100 $166 1,599 East North Central in 016946011 229,100 $137 1,224 East North Central Ini mm 171,300 $116 1,452 East North Central 11 59% 205,100 $113 1,740 East North Central oh m 225,300 $151 1,493 East North Central il W 235,600 $140 1,632 East North Central oh we\East North Central oh summit 185,800 $101 1,847 East North Central mi ionia 193,600 $137 1,416 East North Central il sangamon 213,500 $130 1,643 East North Central mi genesee 194,800 $166 1,173 East North Central oh ashland 188,000 $151 1,246 East North Central oh muskingum 188,300 $94 1,999 East North Central oh tuscarawas 270,700 $149 1,815 East North Central ogle 236,600 $208 1,138 East North Central oh ross 257,200 $127 2.018 East North Central oh washington 324,400 $156 2,081 East North Central mi shiawassee 192,400 $129 1,494 East North Central oh wayne 256,700 $129 1,986 East North Central mi calhoun 266,200 $130 2,042 East North Central mi muskegon 230,400 $131 1,757 East North Central il kankakee 148,700 $115 1,293 East North Central oh pickaway 265,700 $143 1,853 East North Central in lawrence 270,600 $137 1,978 East North Central mi st joseph 188,500 $135 1,397 East North Central wi manitowoc 181.400 $140 1,294 East North Central il champaign 246,700 $121 2,031 East North Central il st clair 201,400 $164 1,225 East North Central oh knox 192,200 $127 1,510 East North Central mi ingbam 222,500 $125 1,777 East North Central oh lorain 226,200 $126 1,789 East North Central il mclean 203,800 $134 1,526 East North Central wi calumet 226,400 $111 2,033 East North Central mi jackson 139,200 $116 1,201 East North Central mi midland 174,500 $151 1,157 East North Central mi isabella 163,000 $125 1,307 East North Central mi marquette 172,500 $120 1,433 East North Central wi wood 266,500 $144 1,853 East North Central in elkhart 202,300 $182 1,113 East North Central mi montcalm 218,300 $105 2.081 East North Central mi monroe 228.600 $136 1,679 East North Central wi grant 243,200 $121 2,014 East North Central oh lake 225,900 $135 1,676 East North Central oh cuyahoga 265, 100 $136 1,947 East North Central mi eaton 189,900 $96 1,976 East North Central oh stark 201.000 $163 1,230 East North Central wi douglas 461.400 $129 3,581 East North Central oh athens 246,400 $158 1,560 East North Central wi marathon 431,200 $119 3,638 East North Central wi milwaukee 184,900 $111 1.666 East North Central dekalb 347,500 $97 3,574 East North Central mi lenawee 191,500 $118 1,628 East North Central in marion 323,300 $95 3,408 East North Central wi fond du lac 135,300 $103 1,312 East North Central in allen 398,000 $113 3,525 East North Central in st joseph 193,000 $111 1,736 East North Central oh hancock 380.300 $94 4.028