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 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 Statistics and Graphs 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 and include a trend line and the regression equation 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?

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Scenario

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 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 Statistics and Graphs 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 and include a trend line and the regression equation
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 Data for East North Central Region**

This table presents real estate data for various counties in the East North Central region of the United States, spanning states such as Ohio (oh), Illinois (il), Michigan (mi), and Wisconsin (wi).

Columns:
- **Region**: Specifies the larger regional location, "East North Central."
- **State**: Abbreviation for the state where the county is located.
- **County**: Name of the county.
- **Listing Price**: The price at which properties are listed (in dollars).
- **$'s per Square Foot**: Average price per square foot.
- **Square Feet**: Average size of homes in square feet.
- **Another Column**: The final column represents a decimal value with unspecified meaning.

Data Explanation:
1. **Range of Listing Prices**: Prices range from $149,700 in Marion, OH to $581,800 in Greene, OH.
2. **Price per Square Foot**: Varies from $94 to $187, with Howard, OH having the lowest and Madison, IN the highest.
3. **Square Feet**: The size spectrum stretches from 1,113 (Elkhart, IN) to 5,146 (Greene, OH).
4. **Mean and Median Values**:
- Listing Price Mean: $260,896.67
- Listing Price Median: $236,150.00
- Square Feet Mean: 2,051.37
- Square Feet Median: 1,687.00
5. **Standard Deviation**:
- Listing Price: $90,491.274, indicating variability in home prices.
- Square Feet: 999.1197, showing variation in home sizes.

This data provides insight into the housing market, showcasing variability in prices, value per square foot, and home sizes across different counties.

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

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