http://www.ck12.org Chapter 9. Regression and Correlation
TABLE9.4:(continued)
Student Number Grade Reading Level
4 4 10
5 1 4- Draw a scatterplot for these data. What type of relationship does this correlation have?
- Use the raw score formula to compute the Pearson correlation coefficient.
A teacher gives two quizzes to his class of 10 students. The following are the scores of the 10 students.
TABLE9.5: Quiz results for ten students.
Student Quiz 1 Quiz 2
1 15 20
2 12 15
3 10 12
4 14 18
5 10 10
6 8 13
7 6 12
8 15 10
9 16 18
10 13 15- Compute the Pearson correlation coefficient(r)between the scores on the two quizzes.
- Find the percentage of the variance(r^2 )in the scores of Quiz 2 associated with the variance in the scores of
Quiz 1. - Interpret bothrandr^2 in words.
- What are the three factors that we should be aware of that affect the size and accuracy of the Pearson correlation
coefficient?
Review Answers
- Various answers are possible. Answers could include scores between two tests, effectiveness of two medica-
tions, behavior patterns, etc. - Various answers are possible.
- Various answers are possible.
- The correlation coefficient measures the nature and the magnitude of the linear relationship between two
variables. - The scatterplot should show the 5 points plotted in a line. This is a perfect correlation.
6.r= 1. 00
7.r= 0. 568
8.r^2 = 0. 323 - The correlation between the two quizzes is positive and is moderately strong. Only a small proportion of the
variance is shared by the two variables( 32 .3%) - Curvilinear relationships, homogeneity of the group and small group size.