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Does a linear relationship exists between two quantitative variables?
Does a linear relationship exists between two quantitative variables?
In this project you will explore the relationship between two quantitative variables using linear regression analysis. You will investigate whether a linear relationship exists, interpret key statistical measures, and present your findings in a clear, professional manner.
Resources
Resources
Data Sources
Data Sources
If you choose OWID, follow this video for a tutorial to transfer data to Stapplet for analysis.
CORGIS: The Collection of Really Great, Interesting, Situated Datasets
Examples
Examples
Examples
Examples
Click through the Cricket Thermometer slideshow below.
See some student presentations here.
Example Questions
Example Questions
the height of a swimmer has an effect on their 50 meter sprint time
the grades one receives in high school can be a good predictor for how one does in college
the salary of an individual has a strong correlation with their level of happiness
Does the number of hours studied (X) predict test scores (Y)?
Is there a relationship between average temperature (X) and ice cream sales (Y)?
Does the GDP of a country (X) predict life expectancy (Y)?
Grading Benchmarks
Grading Benchmarks
Every few days each part will be due sequentially. Please paste a link to your data sources and presentation here. No late work will be accepted for credit, but must be completed at the time of the presentation.
Step-by-Step Guide
Step-by-Step Guide
1. Choose a Research Question
1. Choose a Research Question
Explore a question that investigates the relationship between two quantitative variables. You can use any reliable dataset.
Approval: Run your idea by me or by your classmates before moving forward. Once approved, continue to the next step.
2. Data Collection
2. Data Collection
Source: Use a dataset with at least 30 observations. Your dataset must have two quantitative variables.
Documentation: Clearly describe where your data came from, how it was collected, and include a link to the source.
3. Data Exploration
3. Data Exploration
Univariate Analysis: Start by exploring each variable separately.
Calculate key statistics like mean, median, standard deviation, and range.
Create histograms or boxplots to visualize the distributions.
Correlation: Calculate and interpret the correlation coefficient (r) to determine the strength and direction of the relationship between your variables.
Scatterplot: Create a scatterplot to visualize the relationship between your two variables.
Why do we do this project? Hear what students have to say.
4. Regression Model
4. Regression Model
Least Squares Regression: Fit a least squares regression line to your data.
Report the equation of the line.
Add the regression line to your scatterplot.
Residual Analysis: Create a residual plot to assess the fit of your model. Investigate any patterns in the residuals that suggest a poor model fit.
r² Value: Report and interpret the r² value, which tells you how much of the variability in Y is explained by X.
5. Interpreting Results
5. Interpreting Results
Slope Interpretation: Explain what the slope of your regression line means in the context of your data.
Y-Intercept Interpretation: Discuss the meaning (or lack of meaning) of the y-intercept.
Goodness of Fit: Evaluate whether your model meets the assumptions of linear regression:
Linearity
Independence
Equal spread (homoscedasticity)
Normality of residuals
Predictive Power: Use your model to make predictions and interpret their real-world significance.
6. Discussion & Conclusion
6. Discussion & Conclusion
Model Evaluation: Summarize whether your model provides a good fit for the data. Discuss the strength, limitations, and potential issues with your model.
Real-World Implications: Discuss the broader implications of your findings. How do they answer the research question you posed?
Future Directions: Provide three suggestions on how future studies could improve upon your analysis. For example, suggest collecting more data, using different variables, or employing more advanced statistical techniques.
7. Presentation
7. Presentation
Format: Use the provided Presentation Slide Template or create your own organized, professional slides.
Structure:
Introduction: Research question, data description, and variables.
Data Exploration: Univariate analysis, scatterplot, and correlation.
Regression Model: Line equation, residual plot, and interpretation.
Discussion: Model evaluation, implications, and future directions.
Graphics: Include at least three visual aids: a scatterplot, regression line, and a residual plot.
Conclusion: Present a clear summary of your findings and the next steps for further research.
Old Stuff
Old Stuff
Maybe you are interested in knowing if
Maybe you are interested in knowing if
the height of a swimmer has an effect on their 50 meter sprint time
the grades one receives in high school can be a good predictor for how one does in college
the salary of an individual has a strong correlation with their level of happiness
Here's a list of all of the required elements for your presentation in a list: Presentation Grading Rubric, or if you prefer, below is a written description of these elements.
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