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 Data spreadsheet (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

Describe the report: Give a brief description of the purpose of your report.

Define the question your report is trying to answer.

Explain when using linear regression is most appropriate.

When using linear regression, what would you expect the scatterplot to look like?

Explain the difference between response and predictor variables in a linear regression to justify the selection of variables.

Data Collection

Sampling the data: Select a random sample of 50 houses.

Identify your response and predictor variables.

Scatterplot: Create a scatterplot of your response and predictor variables to ensure they are appropriate for developing a linear model.

Data Analysis

Histogram: For your two variables, create histograms.

Summary statistics: For your two variables, create a table to show the mean, median, and standard deviation.

Interpret the graphs and statistics:

Based on your graphs and sample statistics, interpret the center, spread, shape, and any unusual characteristic (outliers, gaps, etc.) for the two variables.

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

Scatterplot: Provide a graph of the scatterplot of the data with a line of best fit.

Explain if a regression model is appropriate to develop based on your scatterplot.

Discuss associations: Based on the scatterplot, discuss the association (direction, strength, form) in the context of your model.

Identify any possible outliers or influential points and discuss their effect on the correlation.

Discuss keeping or removing outlier data points and what impact your decision would have on your model.

Find r: Find the correlation coefficient (r).

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.

Regression equation: Write the regression equation (i.e., line of best fit) and clearly define your variables.

Interpret regression equation: Interpret the slope and intercept in context.

Strength of the equation: Provide and interpret R-squared.

Determine the strength of the linear regression equation you developed.

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

Summarize findings: In one paragraph, summarize your findings in clear and concise plain language for the CEO to understand. Summarize your results.

Did you see the results you expected, or was anything different from your expectations or experiences?

What changes could support different results, or help to solve a different problem?

Provide at least one question that would be interesting for follow-up research.

# Category: Applied mathematics

## The B&K Real Estate Company sells homes and is currently serving the Southeast region.

This is just a discussion post

6-1 Discussion: Confidence Intervals

The B&K Real Estate Company sells homes and is currently serving the Southeast region. It has recently expanded to cover the Northeast states. The B&K realtors are excited to now cover the entire East Coast and are working to prepare their southern agents to expand their reach to the Northeast.

B&K has hired your company to analyze the Northeast home listing prices in order to give information to their agents about the mean listing price at 95% confidence. Your company offers three analysis packages: one based on a sample size of 100 listings, one based on 1,000 listings, and another based on a sample size of 4,000 listings. Because there is an additional cost for data collection, your company charges more for the package with 4,000 listings than for the package with 100 listings.

Bronze Package – Sample size of 100 listings:

95% confidence interval for the mean of the Northeast house listing price has a margin of error of $24,500

Cost for service to B&K: $2,000

Silver Package – Sample size of 1,000 listings:

95% confidence interval for the mean of the Northeast house listing price has a margin of error of $7,750

Cost for service to B&K: $10,000

Gold Package – Sample size of 4,000 listings:

95% confidence interval for the mean of the Northeast house listing price has a margin of error of $3,900

Cost for service to B&K: $25,000

The B&K management team does not understand the tradeoff between confidence level, sample size, and margin of error. B&K would like you to come back with your recommendation of the sample size that would provide the sales agents with the best understanding of northeast home prices at the lowest cost for service to B&K.

In other words, which option is preferable?

Spending more on data collection and having a smaller margin of error

Spending less on data collection and having a larger margin of error

Choosing an option somewhere in the middle

For your initial post:

Formulate a recommendation and write a confidence statement in the context of this scenario. For the purposes of writing your confidence statement, assume the sample mean house listing price is $310,000 for all packages. “I am [#] % confident the true mean . . . [in context].”

Explain the factors that went into your recommendation, including a discussion of the margin of error

For your response posts to your peers, choose two different confidence intervals for your responses. Do you think the agents would prefer a different confidence interval than their management? What advantages and disadvantages would there be in having different confidence intervals for the agents? Explain your thought process and reasoning in your response.

## Learning Goal: I’m working on a applied mathematics practice test / quiz and nee

Learning Goal: I’m working on a applied mathematics practice test / quiz and need an explanation and answer to help me learn.Texas instruments financial calculator to 9 decimal places.Question 1: Find the proceeds of a promissory note with a maturity value of $1900 due on November 30, 2026, discounted at 3.9% compounded monthly on March 31, percent to 2023.The proceeds are $. enter your response here.(Round to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)Question 2: Two debts, the first of $140 due six months ago and the second of $1000 borrowed one year go for a term of four years at 2.2% compounded annually, are to be replaced by a single payment one year from now. Determine the size of the replacement payment if interest is 3.1% compounded quarterly and the focal date is one year from now.The size of the replacement payment is $. enter your response here.(Round to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)Question 3: Debt payments of $2600 due one year ago and $2400 due two years from now are to be replaced by two equal payments due one year from now and four years from now. What is the size of the equal payments if money is worth 9.6% p.a. compounded semi-annually?The size of each of the two payments is $. enter your response here.(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

## Learning Goal: I’m working on a applied mathematics practice test / quiz and nee

Learning Goal: I’m working on a applied mathematics practice test / quiz and need an explanation and answer to help me learn.Texas instruments financial calculator to 9 decimal places.Question 1: Find the proceeds of a promissory note with a maturity value of $1900 due on November 30, 2026, discounted at 3.9% compounded monthly on March 31, percent to 2023.The proceeds are $. enter your response here.(Round to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)Question 2: Two debts, the first of $140 due six months ago and the second of $1000 borrowed one year go for a term of four years at 2.2% compounded annually, are to be replaced by a single payment one year from now. Determine the size of the replacement payment if interest is 3.1% compounded quarterly and the focal date is one year from now.The size of the replacement payment is $. enter your response here.(Round to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)Question 3: Debt payments of $2600 due one year ago and $2400 due two years from now are to be replaced by two equal payments due one year from now and four years from now. What is the size of the equal payments if money is worth 9.6% p.a. compounded semi-annually?The size of each of the two payments is $. enter your response here.(Round the final answer to the nearest cent as needed. Round all intermediate values to six decimal places as needed.)

## This is just a discussion post 6-1 Discussion: Confidence Intervals The B&K Real

This is just a discussion post

6-1 Discussion: Confidence Intervals

The B&K Real Estate Company sells homes and is currently serving the Southeast region. It has recently expanded to cover the Northeast states. The B&K realtors are excited to now cover the entire East Coast and are working to prepare their southern agents to expand their reach to the Northeast.

B&K has hired your company to analyze the Northeast home listing prices in order to give information to their agents about the mean listing price at 95% confidence. Your company offers three analysis packages: one based on a sample size of 100 listings, one based on 1,000 listings, and another based on a sample size of 4,000 listings. Because there is an additional cost for data collection, your company charges more for the package with 4,000 listings than for the package with 100 listings.

Bronze Package – Sample size of 100 listings:

95% confidence interval for the mean of the Northeast house listing price has a margin of error of $24,500

Cost for service to B&K: $2,000

Silver Package – Sample size of 1,000 listings:

95% confidence interval for the mean of the Northeast house listing price has a margin of error of $7,750

Cost for service to B&K: $10,000

Gold Package – Sample size of 4,000 listings:

95% confidence interval for the mean of the Northeast house listing price has a margin of error of $3,900

Cost for service to B&K: $25,000

The B&K management team does not understand the tradeoff between confidence level, sample size, and margin of error. B&K would like you to come back with your recommendation of the sample size that would provide the sales agents with the best understanding of northeast home prices at the lowest cost for service to B&K.

In other words, which option is preferable?

Spending more on data collection and having a smaller margin of error

Spending less on data collection and having a larger margin of error

Choosing an option somewhere in the middle

For your initial post:

Formulate a recommendation and write a confidence statement in the context of this scenario. For the purposes of writing your confidence statement, assume the sample mean house listing price is $310,000 for all packages. “I am [#] % confident the true mean . . . [in context].”

Explain the factors that went into your recommendation, including a discussion of the margin of error

For your response posts to your peers, choose two different confidence intervals for your responses. Do you think the agents would prefer a different confidence interval than their management? What advantages and disadvantages would there be in having different confidence intervals for the agents? Explain your thought process and reasoning in your response.