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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?

  • A0.48
  • B0.22
  • C0.75
  • D0.83

Q3:

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

  • A1 and 1
  • B1 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?

  • A0.58
  • B0
  • C0.94
  • 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)5.515.725.815.885.916.056.086.106.166.196.316.316.346.486.58
High Jump (m)1.651.771.831.771.771.771.81.771.81.861.861.831.891.861.98

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 𝑆=36.875, 𝑆=73.875, and 𝑆=32.375. 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: 𝑛=8, 𝑥=78, 𝑦=73, 𝑥𝑦=752, 𝑥=792, and 𝑦=735. 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.

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