What is the connections between SAT scores and College GPA?

Welcome: Using Scatter Plots to Analyze SAT Scores and Overall College GPA

Description: A scatter plot is a graphic representation of two variables of data as a set of points in a plane. During this webquest you will create scatter plots using data  and use them to make predictions. 

Grade Level: 9-12 

Curriculum: Statistics 

Keywords: Scatter Plot, Line of Best Fit, Linear Regression, Prediction Equation, Slope, Rate of Change, Y-intercept 

When deciding whether to admit an applicant, colleges take lots of factors, such as grades, sports, activities, leadership positions, awards, teacher recommendations, and test scores, into consideration. Using SAT scores as a basis of whether to admit a student or not has created some controversy. Among other things, people question whether the SATs are fair and whether they predict college performance.

This study examines the SAT and GPA information of 105 students who graduated from a state university with a B.S. in computer science. Using the grades and test scores , can you predict a student's college grades?

Questions to Answer

Can the SAT scores be used to predict college GPA?

1.  A hypothesis, one paragraph in length, on what you believe your research will reveal.

  2. Using the data excel chart, create a scatterplot  on a  sheet of graph paper with appropriate title, labels, and appropriate axis increments.   Please use a pencil.

3.  In looking at your scatter plot, is there a correlation?  If so, what kind?  What does this mean?

4.   How strong would you say the correlation is?  Some of you may have read about the correlation    coefficient.  We are not going to calculate that, but if -1 stood for a perfect negative correlation, 0 stood for absolutely no correlation, and 1 stood for a perfect positive correlation, what would you guess as a correlation coefficient for your graph?

5.   What does this mean?  

6.  In blue colored pencil, draw by freehand your line of best fit.  

7.  Determine the equation of the line of best fit by using the graphing calculator.

8.  Using the line of best fit equation, draw in red the line of best fit based on your line of best fit from the graphing calculator.

10.  Based on your line of best fit(blue and red), how well did you draw your line of best fit as compared to the graphing calculator model? 

11.  If your data had a strong correlation, do you think one outcome causes the other?  In other words, does correlation imply causation?  Explain why.

12.  If a student earned a 826 on their SAT, how can you use the line of best fit equation to predict the students overall college G.P.A?  

13.  If a student earned a 1500 on their SAT, predict their overall college G.P.A?  

14.   A one paragraph written conclusion. Re-analyze your hypothesis…did the statistics back-up your original thoughts? Look at the equations for lines of best fit. What do the slope and y-intercept represent? Go in-depth with an analysis of your research.

he following rubric will be used to grade your project. This will be an 100 point project. There are 5 categories that you will be scored on.

Hypothesis paragraph (10 points)

Scatter plots: Clearly labeled  (30 points)

Lines of best fit (linear regression) and their equations.  (20 points)

Questions:  Answer questions   (30 points)

Conclusion paragraph (10 points)

See attached rubric.  

Scatter plots can be used to predict many real world situations. You can earn an extra 2 bonus points if you can list 2 different relationships and hypothesize their type of correlation that you might encounter or need during high school. Remember though, scatter plots show the relationship between 2 variables, not if one causes the other. So for those of you looking to use a scatter plot to find a date, it's probably not going to help you!