Question

Some students are good in mathematics and others are better at reading or writing. The question is whether there is any relationship between a student’s ability in math and his/her ability in reading or writing. The SAT, a standardized test for college admissions that is widely used in the United States, has three sections, Math, Critical Reading, and Writing. The table below contains SAT Math, Writing, and Critical Reading test scores for 20 randomly chosen students accepted by a university.

Math                         Writing                  Reading

440                           410                           410

550                         570                           520

520                         520                           540

420                         470                           410

550                         620                           530

650                         560                           560

610                         620                           550

610                         520                           600

340                           470                           400

600                           540                           620

680                           580                           580

440                           430                           470

440                           450                           370

390                           430                           390

460                           600                           600

460                           520                           500

520                           570                           580

540                           530                           570

420                           430                           470

550                           480                           530

1. Copy and Paste your data into stat crunch. Label each column.

2. Create a scatter plot for the Math Scores (x) and Writing Scores (y). Go to statàregressionàsimple linear. Select x and y and “compute” click the arrow at the bottom to see the scatter plot. Copy a paste a screen shot of your scatter plot

3. Repeat Step 2, but create a scatter plot for Math Scores (x) and Reading Scores (y). Copy and paste a screen shot of your scatter plot.

4. Looking at the two scatter plots, which appear to be more strongly correlated, Math and Writing or Math and Reading? Explain.

5. Compare the r-values for Math and Writing to the r-value for Math and reading. Which appear to be more strongly correlated Math and Writing or Math and Reading? Explain how you can tell using the r-values.

Answer 1

1) Scatter plot for Math scores (x) and Writing scores (y):

2) Scatter plot for Math Score (y) vs Reading Score (x):

3) Looking at the two scatter plots, Math and Reading scores appear to be more strongly correlated, since the scatter is lesser in that case.

4) Correlation between Math and Reading values = 0.784

Correlation between Math and Writing values = 0.68

Now, looking at the r-values, Math and Reading values are more strongly correlated. Since r-value tells us the strength of linear relationship between the two variables, the ones with the higher r-value are more strongly correlated.