# Lesson Worksheet: Pearson’s Correlation Coefficient Mathematics • 9th Grade

In this worksheet, we will practice calculating and using Pearson’s correlation coefficient, 𝑟, to describe the strength and direction of a linear relationship.

Q1:

Which of the following is the most appropriate interpretation of a product-moment correlation coefficient of 0.8?

• Aa strong negative linear correlation
• Ba moderate negative linear correlation
• Ca moderate positive linear correlation
• Da strong positive linear correlation
• Eno correlation

Q2:

Which of the following correlation coefficients indicates the weakest inverse correlation?

• A
• B
• C
• D

Q3:

Between which two values does the product-moment correlation coefficient lie?

• A and 1
• B and 0
• CIt depends on the scale of the data.
• D0 and 100
• E0 and 1

Q4:

What is the most likely value of the product-moment correlation coefficient for the data shown in the diagram? • A
• B0
• C
• D0.78
• E0.37

Q5:

True or False: The steeper the slope of a regression line, the larger the correlation coefficient between the two variables.

• ATrue
• BFalse

Q6:

If all points on a scatter diagram lie directly on a straight line of positive slope, what is the value of the product-moment correlation coefficient for this data set?

Q7:

If all points on a scatter diagram lie directly on a straight line of negative slope, what is the value of the product-moment correlation coefficient for this data set?

Q8:

The data table shows the high jump and long jump results achieved by 15 competitors in the women’s heptathlon in the 2016 Rio Olympics.

 Long Jump (m) High Jump (m) 5.51 5.72 5.81 5.88 5.91 6.05 6.08 6.1 6.16 6.19 6.31 6.31 6.34 6.48 6.58 1.65 1.77 1.83 1.77 1.77 1.77 1.8 1.77 1.8 1.86 1.86 1.83 1.89 1.86 1.98

Calculate, to the nearest thousandth, the value of the product-moment correlation coefficient between the long jump and high jump results.

What does this correlation coefficient reveal about the relationship between the long jump and high jump results?

• AThere is a moderate negative linear correlation between the long jump and high jump results.
• BThere is a strong positive linear correlation between the long jump and high jump results.
• CThere is a moderate positive linear correlation between the long jump and high jump results.
• DThere is a strong negative linear correlation between the long jump and high jump results.
• EThere is no real correlation between the long jump and high jump results.

Q9:

A data set has summary statistics , , and . Calculate the product-moment correlation coefficient for this data set, giving your answer correct to three decimal places.

Q10:

A data set can be summarized by the following: , , , , , and . Calculate the product-moment correlation coefficient for this data set, giving your answer correct to three decimal places.

This lesson includes 20 additional questions and 63 additional question variations for subscribers.