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. 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 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.
   1. Define the question your report is trying to answer.
   2. Explain when using linear regression is most appropriate.
      1. When using linear regression, what would you expect the scatterplot to look like?
   3. 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.
   1. Identify your response and predictor variables.
2. Scatterplot: Create 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, create a table to show the mean, median, and standard deviation.
3. Interpret the graphs and statistics:
   1. Based on your graphs and sample statistics, interpret the center, spread, shape, and any unusual characteristic (outliers, gaps, etc.) for the two variables.
   2. 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.
   1. Explain if a regression model is appropriate to develop based on your scatterplot.
2. Discuss associations: Based on the scatterplot, discuss the association (direction, strength, form) in the context of your model.
   1. Identify any possible outliers or influential points and discuss their effect on the correlation.
   2. Discuss keeping or removing outlier data points and what impact your decision would have on your model.
3. Find r: Find the correlation coefficient (r).
   1. 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.

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 interpret R-squared.
   1. Determine the strength of the linear regression equation you developed.
4. 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.
   1. Did you see the results you expected, or was anything different from your expectations or experiences?
      1. What changes could support different results, or help to solve a different problem?
      2. Provide at least one question that would be interesting for follow-up research.
         

Region State County listing price $'s per square foot square feet East North Central il dekalb 347,500 $97 3,574 0.482482 East North Central oh wayne 256,700 $129 1,986 0.349674 East North Central oh pickaway 265,700 $143 1,853 0.915247 East North Central oh greene 581,800 $113 5, 146 0.084022 East North Central mi shiawassee 192,400 $129 1,494 0.345553 East North Central in madison 229, 100 $187 1,224 0.874273 East North Central wi manitowoc 181,400 $140 1,294 0.636274 East North Central in howard 304,300 $152 1,996 0.428493 East North Central il madison 254,500 $156 1,628 0.459988 East North Central il vermilion 254,500 $156 1,632 0.326457 East North Central in marion 323,300 $95 3,408 0.120861 East North Central in lake 470,600 $109 4,316 0.828438 East North Central oh scioto 204,200 $131 1,562 0.760423 East North Central mi ingham 222,500 $125 1,777 0.760877 East North Central in henry 235,000 $148 1,588 0.489688 East North Central oh cuyahoga 265, 100 $136 1,947 0. 151024 East North Central il winnebago 236,700 $140 1,692 0.549534 East North Central oh marion 149,700 $1 16 1,296 0.939514 East North Central oh muskingum 188,300 $94 1,999 0.422032 East North Central oh hancock 380,300 $94 4,028 0.218561 East North Central in vanderburgh 214, 100 $134 1,596 0.959347 East North Central mi isabella 163,000 $125 1,307 0.717554 East North Central il henry 257,700 $123 2,087 0.374139 East North Central in delaware 221,600 $134 1,651 0.652486 East North Central oh washington 324,400 $156 2,081 0.812501 East North Central oh seneca 211,900 $168 1,263 0.992269 East North Central oh richland 248,900 $132 1,880 0.45392 East North Central in elkhart 202,300 $182 1, 113 0.0214 East North Central il stephenson 235,600 $140 1,682 0.980118 East North Central in wayne 203,800 $141 1,441 0.174717 Mean 260,896.67 Mean 2,051.37 Median 236, 150.00 Median 1,687.00 Standard Deviation 90,491.2474 Standard Deviation 999. 1197