Overview
Recall that samples are used to generate a statistic, which businesses use to estimate the population parameter. You have learned how to take samples from populations and use them to produce statistics. For two quantitative variables, businesses can use scatterplots and the correlation coefficient to explore a potential linear relationship. Furthermore, they can quantify the relationship in a regression equation.
Prompt
This assignment picks up where the Module Two assignment left off and will use components of that assignment as a foundation.
You have submitted your initial analysis to the sales team at D.M. Pan Real Estate Company. You will continue your analysis of the provided Real Estate Data spreadsheet using your selected region to complete your analysis. You may refer back to the initial report you developed in the Module Two Assignment Template to continue the work. This document and the National Statistics and Graphs spreadsheet will support your work on the assignment.
Note: In the report you prepare for the sales team, the dependent, or response, variable (y) should be the listing price and the independent, or predictor, variable (x) should be the square feet.
Using the Module Three Assignment Template, specifically address the following:
- Regression Equation: Provide the regression equation for the line of best fit using the scatterplot from the Module Two assignment.
- Determine r: Determine r and what it means. (What is the relationship between the variables?)
- Determine the strength of the correlation (weak, moderate, or strong).
- Discuss how you determine the direction of the association between the two variables.
- Is there a positive or negative association?
- What do you see as the direction of the correlation?
- Examine the Slope and Intercepts: Examine the slope{“version”:”1.1″,”math”:”<math xmlns=”http://www.w3.org/1998/Math/MathML”><msub><mi>b</mi><mn>1</mn></msub></math>”} and intercept {“version”:”1.1″,”math”:”<math xmlns=”http://www.w3.org/1998/Math/MathML”><msub><mi>b</mi><mn>0</mn></msub></math>”}.
- Draw conclusions from the slope and intercept in the context of this problem.
- Does the intercept make sense based on your observation of the line of best fit?
- Determine the value of the land only.
Note: You can assume, when the square footage of the house is zero, that the price is the value of just the land. This happens when x=0, which is the y-intercept. Does this value make sense in context?
- Draw conclusions from the slope and intercept in the context of this problem.
- Determine the R-squared Coefficient: Determine the R-squared value.
- Discuss what R-squared means in the context of this analysis.
- Conclusions: Reflect on the Relationship: Reflect on the relationship between square feet and sales price by answering the following questions:
- Is the square footage for homes in your selected region different than for homes overall in the United States?
- For every 100 square feet, how much does the price go up (i.e., can you use slope to help identify price changes)?
- What square footage range would the graph be best used for?
Guidelines for Submission
Submit your completed Module Three Assignment Template as a Word document that includes your response, supporting charts/graphs, and your Excel file.
| Criteria | Exemplary | Proficient | Needs Improvement | Not Evident | Value |
|---|---|---|---|---|---|
| Regression Equation | N/A | Provides the regression equation for the line of best fit (100%) | Shows progress toward proficiency, but with errors or omissions; areas for improvement may include an inaccurate equation (55%) | Does not attempt criterion (0%) | 10 |
| Determine r | Exceeds proficiency in an exceptionally clear manner (100%) | Describes the direction, strength of correlation, and association between the variables (85%) | Shows progress toward proficiency, but with errors or omissions; areas for improvement may include missing one or more of the following: direction, strength of correlation, or association between the variables (55%) | Does not attempt criterion (0%) | 20 |
| Examine the Slope and Intercept | Exceeds proficiency in an exceptionally clear manner (100%) | Draws conclusions from the slope and intercept in context, makes predictions, determines the value of only the land (85%) | Shows progress toward proficiency, but with errors or omissions; areas for improvement may include missing one or more of the following: conclusions from the slope and intercept in context, predictions, or the value of only the land (55%) | Does not attempt criterion (0%) | 20 |
| Determine the R-squared Coefficient | Exceeds proficiency in an exceptionally clear manner (100%) | Determines the R-squared coefficient and explains it in context (85%) | Shows progress toward proficiency, but with errors or omissions; areas for improvement may include an inaccurate determination of the R-squared coefficient or an explanation that is out of context (55%) | Does not attempt criterion (0%) | 20] |
| Conclusions: Reflect on the Relationship | Exceeds proficiency in an exceptionally clear, insightful, or sophisticated manner (100%) | Reflects on the relationship between square feet and sales price (85%) | Shows progress toward proficiency, but with errors or omissions; areas for improvement may include a reflection on the relationship between variables that is missing components (55%) | Does not attempt criterion (0%) | 20 |
| Articulation of Response | Exceeds proficiency in an exceptionally clear, insightful, sophisticated, or creative manner (100%) | Clearly conveys meaning with correct grammar, sentence structure, and spelling, demonstrating an understanding of audience and purpose (85%) | Shows progress toward proficiency, but with errors in grammar, sentence structure, and spelling, negatively impacting readability (55%) | Submission has critical errors in grammar, sentence structure, and spelling, preventing understanding of ideas (0%) | 10 |
| Total: | 100% |
