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 predictor (x) and response (y) variables in a linear regression to justify the selection of variables.

Data Collection

1. Sampling the data: Select a random sample of 50 houses. Describe how you obtained your sample data (provide Excel formulas as appropriate).
   1. Identify your predictor and response variables.
2. Scatterplot: provide a scatterplot of your predictor and response variables to ensure they are appropriate for developing a linear model.

Data Analysis

1. Histogram: provide a histogram for each of the two variables.
2. Summary statistics: For your two variables, provide 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 house sales and square footage.
   2. Compare and contrast the center, shape, spread, and any unusual characteristic for your sample of house sales with the national population (under Supporting Materials, see the National Summary Statistics and Graphs House Listing Price by Region PDF). Determine whether your sample is representative of national housing market sales.

Develop Your Regression Model

1. Scatterplot: Provide a scatterplot of the variables with a line of best fit and regression equation.
   1. Based on your scatterplot, explain if a regression model is appropriate.
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. Calculate r: Calculate 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. For example, answer the questions: what does the slope represent in this situation? What does the intercept represent? Revisit the Scenario above.
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 assumed square footage of your home at 1500 square feet.

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?
   2. What changes could support different results, or help to solve a different problem?
   3. 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	in	grant	219,500	$116	1,898
East North Central	il	vermilion	254,500	$156	1,632
East North Central	in	henry	235,000	$148	1,588
East North Central	in	wayne	203,800	$141	1,441
East North Central	il	coles	220,800	$117	1,893
East North Central	il	macoupin	197,600	$111	1,783
East North Central	in	vigo	165,800	$122	1,362
East North Central	oh	jefferson	246,500	$136	1,814
East North Central	il	jackson	154,300	$105	1,463
East North Central	oh	marion	149,700	$116	1,296
East North Central	mi	bay	145,100	$117	1,239
East North Central	il	whiteside	283,700	$136	2,087
East North Central	oh	trumbull	243,000	$133	1,827
East North Central	in	madison	229,100	$187	1,224
East North Central	il	knox	205,100	$118	1,740
East North Central	il	stephenson	235,600	$140	1,682
East North Central	il	macon	212,900	$128	1,659
East North Central	in	delaware	221,600	$134	1,651
East North Central	il	henry	257,700	$123	2,087
East North Central	oh	seneca	211,900	$168	1,263
East North Central	oh	darke	160,800	$114	1,416
East North Central	oh	scioto	204,200	$131	1,562
East North Central	oh	belmont	172,500	$101	1,710
East North Central	oh	sandusky	253,900	$146	1,738
East North Central	il	rock island	166,300	$127	1,305
East North Central	oh	clark	240,500	$137	1,752
East North Central	oh	columbiana	241,400	$164	1,469
East North Central	in	howard	304,300	$152	1,996
East North Central	oh	richland	248,900	$132	1,880
East North Central	il	peoria	187,900	$131	1,434
East North Central	il	la salle	311,100	$154	2,015
East North Central	il	madison	254,500	$156	1,628
East North Central	mi	wayne	213,800	$172	1,243
East North Central	in	vanderburgh	214,100	$134	1,596
East North Central	oh	mahoning	207,500	$123	1,688
East North Central	il	williamson	171,600	$141	1,218
East North Central	il	winnebago	236,700	$140	1,692
East North Central	il	adams	266,100	$166	1,599
East North Central	mi	saginaw	171,800	$118	1,452
East North Central	oh	montgomery	225,300	$151	1,493
East North Central	oh	allen	227,600	$147	1,550
East North Central	oh	lucas	228,300	$115	1,978
East North Central	oh	ashtabula	177,000	$107	1,658
East North Central	oh	lawrence	248,300	$156	1,587
East North Central	oh	huron	199,700	$147	1,359
East North Central	il	tazewell	278,700	$165	1,693
East North Central	oh	summit	185,800	$101	1,847
East North Central	il	sangamon	213,500	$130	1,643
East North Central	oh	ashland	188,000	$151	1,246
East North Central	oh	tuscarawas	270,700	$149	1,815