Introduction
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
Task
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?
Process
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.
| SAT Scores | univ_GPA |
| 1229 | 3.52 |
| 1070 | 2.91 |
| 1086 | 2.4 |
| 1287 | 3.47 |
| 1130 | 3.47 |
| 1030 | 2.37 |
| 1131 | 2.4 |
| 1095 | 2.24 |
| 1135 | 3.02 |
| 1206 | 3.32 |
| 1333 | 3.59 |
| 1160 | 2.54 |
| 1186 | 3.19 |
| 1243 | 3.71 |
| 1261 | 3.58 |
| 1325 | 3.4 |
| 1384 | 3.73 |
| 1364 | 3.49 |
| 1065 | 2.25 |
| 1106 | 2.37 |
| 1175 | 3.29 |
| 1161 | 3.19 |
| 1226 | 3.28 |
| 1176 | 3.37 |
| 1421 | 3.61 |
| 1450 | 3.81 |
| 1116 | 2.4 |
| 1069 | 2.21 |
| 1331 | 3.58 |
| 1441 | 3.51 |
| 1415 | 3.62 |
| 1303 | 3.6 |
| 1420 | 3.65 |
| 1362 | 3.76 |
| 1061 | 2.27 |
| 1107 | 2.35 |
| 1272 | 3.17 |
| 1353 | 3.47 |
| 1164 | 3 |
| 1085 | 2.74 |
| 1231 | 3.37 |
| 1289 | 3.54 |
| 1187 | 3.28 |
| 1102 | 3.39 |
| 1221 | 3.28 |
| 1122 | 3.19 |
| 1064 | 2.52 |
| 1135 | 3.08 |
| 1192 | 3.01 |
| 1255 | 3.42 |
| 1234 | 3.6 |
| 1114 | 2.4 |
| 1093 | 2.83 |
| 1092 | 2.38 |
| 1087 | 3.21 |
| 1176 | 2.24 |
| 1224 | 3.4 |
| 1175 | 3.07 |
| 1220 | 3.52 |
| 1181 | 3.47 |
| 1112 | 3.08 |
| 2362 | 3.38 |
| 1257 | 3.41 |
| 1387 | 3.64 |
| 1336 | 3.71 |
| 1250 | 3.01 |
| 1265 | 3.37 |
| 1106 | 2.34 |
| 1275 | 3.29 |
| 1256 | 3.4 |
| 1366 | 3.38 |
| 1420 | 3.28 |
| 1249 | 3.31 |
| 1307 | 3.42 |
| 1390 | 3.39 |
| 1293 | 3.51 |
| 1155 | 3.17 |
| 1063 | 3.2 |
| 1379 | 3.41 |
| 1280 | 3.29 |
| 1074 | 3.17 |
| 1173 | 3.12 |
| 1210 | 3.71 |
| 1293 | 3.5 |
| 1354 | 3.34 |
| 1291 | 3.48 |
| 1279 | 3.44 |
| 1178 | 3.59 |
| 1194 | 3.28 |
| 1163 | 3 |
| 1034 | 3.42 |
| 1202 | 3.41 |
| 1208 | 3.49 |
| 1147 | 3.28 |
| 1242 | 3.17 |
| 1374 | 3.24 |
| 1113 | 2.34 |
| 1334 | 3.28 |
| 1105 | 2.29 |
| 1109 | 2.08 |
| 1195 | 3.64 |
| 1375 | 3.42 |
| 1372 | 3.25 |
| 1120 | 2.76 |
| 1042 | 3.41 |
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.
Evaluation
The 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 (20 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 (20 points)
RUBRIC FOR COMPLETING A WEBQUEST
Student name: __________________________
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|
Needs Improvement |
Developing |
Admirable |
Exceptional
|
Score |
|
Hypotheses (20 points) |
0 The type of correlation is hypothesized. Little to no rational is given though. |
5 The type of correlation is hypothesized. Reasons for this hypothesis is unclear and lacks reasoning. |
10 The type of correlation is hypothesized. Reasons for this hypothesis is unclear and lacks reasoning. |
The type of correlation is hypothesized using at least 3 rational reasons. |
|
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Scatterplot with freehand line of best fit(blue colored pencil) (30 points) |
0 The scatter plot was accurate, labeled, and readable. |
10 The scatter plot had an important error and/or was not labeled/readable. |
20 The scatter plot was semi-accurate or not easily read |
30 The scatter plot was accurate, labeled, and readable. |
|
|
Line of Best Fit Equation and line of best fit based on line of best fit equation (20 points) |
0 The equation for the line of best fit was not calculated and the line of best fit was not drawn on the graph paper. |
5 The equation for the line of best fit was incorrect and the line of best fit was accurately drawn of the graph paper. |
10 The equation for the line of best fit had a slight error and the line of best fit was drawn accurately on graph paper based on the slight error. |
20 The equation for the line of best fit was correct and the line of best fit was drawn accurately on the graph paper |
|
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Answer Questions (30 points) |
0 All questions were incorrectly answered and all predictions were incorrect.
|
10 The majority of the questions were incorrectly answered and come predictions were incorrect. |
20 The majority of questions were answered correctly and correct prediction were made. |
30 All questions were answered correctly and correct prediction were made. |
|
|
Conclusion paragraph (20 points) |
0 There is no explanation on why it's that type of correlation. Paragraph does not expand on or analyze the results of their research.
|
5 A good paragraph that includes what type of correlation exists and hypothesizes. Paragraph only includes required information and does not expand on or analyze the results of their research. |
10 A well-written paragraph that discusses the results of their research. Includes what type of correlation exists and hypothesizes why. |
20 Paragraph that goes in-depth when analyzing the results of their research. Includes what type of correlation exists and hypothesizes why. |
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TOTAL POINTS: _______________/120
Conclusion
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!
Credits
Resources:
How to make a scatterplot :
Using graphing calculator to find the line of best fit