Linear Regression
In this project you will perform regression analysis on data to develop a mathematical model that relates two variables. Then you will use this model to make predictions.
Objectives
- Find and use data directly from the internet
- Produce a scatter plot of the data
- Perform a regression analysis to find the equation of the line that best fits the data
- Display the results, plotted data and the regression equation together for visual comparison
- Use the model to make predictions
- Make any conclusions about the data
Steps for the Project
1. Find and select your data
You are responsible for finding data. Check with your teacher to be sure the data you have selected would be a good fit for the project. Find a minimum of 20 data points.
2. Create a scatter plot.
You need to verify the presence of a relationship between the two variables. Make a scatter plot with these two variables, and show your independent and dependent variables. Label the axes and the graph accordingly (y vs. x).
3. Regression analysis.
Input your data onto a graph. Calculate the regression equation and the correlation coefficient. Add the regression line to your scatter plot.
4. Make conclusions.
Explain the significance of your results and how you can interpret them. Describe what sort of correlation exists. Is there a strong, weak, or no correlation in the data?
5. Apply it to the real world.
How might your conclusions impact the real world? What sorts of useful applications might you be able to make from your model? Write about ways that you might take advantage of the data. If you feel your data was not particularly useful due to a low correlation coefficient, write about what other patterns you may see in the scatter plot or how it is useful to know that there is little correlation between the variables.
6. Presentation.
You will present your results in 1-2 page written report and on a poster. The written report includes a table of your raw data, your calculations for finding the regression line/equation [in slope-intercept form: y = mx + b], any predictions, analysis and/or impact on the real world, and a reflection about the whole project. The poster should include a title, a scatterplot graph with the regression line, pictures to enhance your topic, the type of correlation, and possible predictions/impact on the world.
Checklist
- Data table
- Scatter plot with regression line
- Regression equation and correlation coefficient
- 1 page report and reflection [raw data, regression equation, prediction, analysis and/or impact on the real world, reflection]
- Poster [scatter graph with regression line, appropriate pictures, predictions, correlation]
Rubric
|
1 |
2 |
3 |
4 |
|
|
Representation of Data
|
Minimal data; data/scatter plots missing |
Some missing data/scatter plots |
Data present and accurate save for minor errors |
Data accurately portrayed in tables and graphs |
|
Application of Regression
|
Regression not performed |
Regression results inaccurate due to faulty calculation |
Regression results slightly off due to data entry |
Regression results perfectly accurate |
|
Conclusions from Results
|
Displays no evidence of understanding of conclusions |
Misrepresents results by drawing conflicting conclusions |
Results largely interpreted correctly with some minor misinterpretations |
Shows clear understanding of the results and why they were reached |
|
Real World Interpretation
|
Makes no connection to the real world |
Has some ideas of how data connects to real world situation |
Shows connections to real world but could be more thorough |
Strongly connects results to real world applications |
|
Presentation
|
Written report and/or poster is missing and demonstrates little understanding of the requirements. present |
Written report and poster show demonstrate a progressing understanding, but or cannot explain ideas thoroughly |
Written report and poster demonstrate a proficient understanding of the project and is able to communicate well |
Written report and poster demonstrate an exemplary understanding of project and shows considerable time and thought invested |
Data:
|
Drivers |
races |
wins |
|
Dale Earnhardt Jr. |
36 |
4 |
|
Austin Dillon |
9 |
0 |
|
Clint Bowyer |
24 |
0 |
|
Jeff Gordon |
46 |
6 |
|
Kevin Harvick |
33 |
2 |
|
Kurt Busch |
33 |
1 |
|
Ron Hornaday Jr. |
1 |
0 |
|
Joey Logano |
18 |
1 |
|
Denny Hamlin |
24 |
1 |
|
Corey LaJoie |
2 |
0 |
|
Jimmie Johnson |
32 |
3 |
|
Ricky Stenhouse Jr. |
11 |
1 |
|
Matt Crafton |
1 |
0 |
|
Elliott Sadler |
27 |
0 |
|
Kyle Busch |
25 |
1 |
|
Tony Stewart |
35 |
4 |
|
Matt Kenseth |
36 |
2 |
|
Paul Menard |
21 |
0 |
|
Greg Biffle |
28 |
1 |
|
Kasey Kahne |
28 |
0 |
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