10.1.6: Correlation
- Page ID
- 63627
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Semester Project – Assignment 6: Correlation and Scatterplot Analysis
In this portion of your project, you will explore the relationship between two key quantitative variables in your dataset: rental price and square footage of 1-bedroom apartments. Your goal is to measure the strength and direction of any relationship using a scatterplot, calculate the correlation coefficient (r), and interpret your findings in a real-world context.
This analysis introduces the concepts of correlation and regression, which can inform future predictions and deeper understanding of data patterns. You’ll also explore the possibility of other variables influencing rental price and describe how they might positively or negatively relate.
Objectives
- Analyze paired quantitative data using correlation and regression tools
- Create a scatterplot visualizing relationship between square footage and price
- Calculate and interpret the correlation coefficient (r)
- Identify possible outliers or surprising patterns in the plot
- Use technology to deepen understanding of relationships between numerical variables
🧠Assignment Steps
-
Create a scatterplot of price vs. square footage using Excel, Google Sheets, or another tool. Your graph must include:
- Clearly labeled axes (e.g., X-axis: square footage, Y-axis: price)
- A descriptive and meaningful title (e.g., “Rental Price vs. Square Footage in Lakewood & Golden”)
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Calculate the correlation coefficient (r) for your paired dataset. Use technology to determine:
- The r-value (strength & direction)
- Whether it is statistically significant (use a critical value table or p-value)
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Answer the following reflection questions:
- Interpret the correlation: Is it strong, weak, or moderate? Is it positive or negative? What does that tell you about the relationship between square footage and rental price in your sample?
- Contextualize the scatterplot: What story does it tell about the local rental market? Are there outliers, holes, or clusters that influence your interpretation?
- Identify a negatively correlated variable: What variable (not square footage) might be inversely related to rental price? Make a suggestion and support your reasoning.
What to Include in Your Final Paper (Draft Version)
This analysis forms the foundation for your paper section titled: Exploring Relationships Between Variables. Be sure to include:
- Your scatterplot image or embedded chart
- The calculated correlation coefficient and significance level (if tested)
- Written interpretation of the strength and direction of the relationship
- Discussion of any visible outliers and their potential impact
- Your thoughts on other possible influencing variables, with reasoning
Helpful Tips
- r-values near +1 or -1 reflect strong correlations. An r of 0.75 means a strong positive trend. An r of -0.6 would suggest a moderately strong negative correlation.
- Don’t forget to label ALL axes; “Price” and “Square Footage” should include units (e.g., $USD, sq. ft.)
- Outliers can distort your value of r. Check your scatterplot visually for values that “don’t fit,” which could be apartments much larger or smaller than others in your sample.
- If you’re curious about building a regression line (optional), Excel and Google Sheets make it easy to add a trendline and show the equation on the chart.
- Your possible "negatively correlated" influences might include things like being farther from downtown, stricter pet policies, or lack of amenities.
Submission Instructions
- Submit your work as a Google Sheet, Excel file, slide screenshot, or document
- Include your scatterplot, r-value, and all written reflection responses
- File name format:
LastName_CorrelationAnalysis - Upload to the “Project Assignments” folder in the LMS