Smart businesses in all industries use data to provide an intuitive analysis of how they can get a competitive advantage. The real estate industry heavily uses linear regression to estimate home prices, as cost of housing is currently the largest expense for most families. Additionally, in order to help new homeowners and home sellers with important decisions, real estate professionals need to go beyond showing property inventory. They need to be well versed in the relationship between price, square footage, build year, location, and so many other factors that can help predict the business environment and provide the best advice to their clients.

Prompt

You have been recently hired as a junior analyst by D$.$M$.$ Pan Real Estate Company. The sales team has tasked you with preparing a report that examines the relationship between the selling price of properties and their size in square feet. You have been provided with a Real Estate Data Spreadsheet spreadsheet that includes properties sold nationwide in recent years. The team has asked you to select a region, complete an initial analysis, and provide the report to the team.

Note: In the report you prepare for the sales team, the response variable $($y$)$ should be the listing price and the predictor variable $($x$)$ should be the square feet.

Specifically you must address the following rubric criteria, using the Module Two Assignment Template:

Generate a Representative Sample of the Data

Select a region and generate a simple random sample of $30$ from the data.

Report the mean, median, and standard deviation of the listing price and the square foot variables.

Analyze Your Sample

Discuss how the regional sample created is or is not reflective of the national market.

Compare and contrast your sample with the population using the National Summary Statistics and Graphs Real Estate Data PDF document.

Explain how you have made sure that the sample is random.

Explain your methods to get a truly random sample.

Generate Scatterplot

Create a scatterplot of the x and y variables noted above. Include a trend line and the regression equation. Label the axes.

Observe patterns

Answer the following questions based on the scatterplot:

Define x and y$.$ Which variable is useful for making predictions?

Is there an association between x and y$?$ Describe the association you see in the scatter plot.

What do you see as the shape $($linear or nonlinear$)?$

If you had a $1,800$ square foot house, based on the regression equation in the graph, what price would you choose to list at$?$

Do you see any potential outliers in the scatterplot?

Why do you think the outliers appeared in the scatterplot you generated?

What do they represent?

Real Estate County Data for $2019$

$2019$ Data $($n$=1000)$

Region State County listing price $$\text{'}$s per square foot square feet

East North Central in grant $219,500$ $$1161,898$

East North Central il vermilion $254,500$ $$1561,632$

East North Central in henry $235,000$ $$1481,588$

East North Central in wayne $203,800$ $$1411,441$

East North Central il coles $220,800$ $$1171,893$

East North Central il macoupin $197,600$ $$1111,783$

East North Central in vigo $165,800$ $$1221,362$

East North Central oh jefferson $246,500$ $$1361,814$

East North Central il jackson $154,300$ $$1051,463$

East North Central oh marion $149,700$ $$1161,296$

East North Central mi bay $145,100$ $$1171,239$

East North Central il whiteside $283,700$ $$1362,087$

East North Central oh trumbull $243,000$ $$1331,827$

East North Central in madison $229,100$ $$1871,224$

East North Central il knox $205,100$ $$1181,740$

East North Central il stephenson $235,600$ $$1401,682$

East North Central il macon $212,900$ $$1281,659$

East North Central in delaware $221,600$ $$1341,651$

East North Central il henry $257,700$ $$1232,087$

East North Central oh seneca $211,900$ $$1681,263$

East North Central oh darke $160,800$ $$1141,416$

East North Central oh scioto $204,200$ $$1311,562$

East North Central oh belmont $172,500$ $$1011,710$

East North Central oh sandusky $253,900$ $$1461,738$

East North Central il rock island $166,300$ $$1271,305$

East North Central oh clark $240,500$ $$1371,752$

East North Central oh columbiana $241,400$ $$1641,469$

East North Central in howard $304,300$ $$1521,996$

East North Central oh richland $248,900$ $$1321,880$

East North Central il peoria $187,900$ $$1311,434$

East North Central il la salle $311,100$ $$1542,015$

East North Central il madison $254,500$ $$1561,628$

East North Central mi wayne $213,800$ $$1721,243$

East North Central in vanderburgh $214,100$ $$1341,596$

East North Central oh mahoning $207,500$ $$1231,688$

East North Central il williamson $171,600$ $$1411,218$

East North Central il winnebago $236,700$ $$1401,692$

East North Central il adams $266,100$ $$1661,599$

East North Central mi saginaw $171,800$ $$1181,452$

East North Central oh montgomery $225,300$ $$1511,493$

East