Worksheet: Linear Correlation Coefficient

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

Q1:

Which of the following correlation coefficients indicates the strongest correlation?

  • A0.43
  • B0.31
  • C0.69
  • D0.71

Q2:

What is the value of the product-moment correlation coefficient for the data set shown?

Q3:

Which of the following correlation coefficients indicates the weakest correlation?

  • A0.68
  • B0.58
  • C0.48
  • D0.9

Q4:

Which of the following correlation coefficients indicates the weakest correlation?

  • A 0 . 8 8
  • B0.77
  • C 0 . 4 9
  • D 0 . 2 6

Q5:

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

  • A 0 . 2 2
  • B 0 . 7 5
  • C 0 . 8 3
  • D 0 . 4 8

Q6:

What is the value of the product-moment correlation coefficient for the data set shown?

Q7:

What is the most likely value of the product-moment correlation coefficient for the data shown in the diagram?

  • A 0 . 5 8
  • B0
  • C 0 . 9 4
  • D0.78
  • E0.37

Q8:

What is the most likely value of the product-moment correlation coefficient for the data shown in the diagram?

  • A0
  • B0.78
  • C0.37
  • D 0 . 9 4
  • E 0 . 5 8

Q9:

What is the most likely value of the product-moment correlation coefficient for the data shown in the diagram?

  • A 0 . 5 8
  • B0.78
  • C 0 . 9 4
  • D0.37
  • E0

Q10:

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?

Q11:

Which of the following correlation coefficients indicates the strongest correlation?

  • A 0 . 3 3
  • B 0 . 8 7
  • C 0 . 1 4
  • D 0 . 8 8

Q12:

The scatterplot shows the high jump and long jump results achieved by 15 competitors in the women’s heptathlon at the 2016 Olympics in Rio de Janeiro.

The correlation coefficient for this dataset is 0.859. What is the correct interpretation of this correlation coefficient?

  • A Being good at the long jump causes a competitor to be better at the high jump.
  • B There is strong positive linear correlation between performance in the high jump and the long jump.
  • C There is strong negative linear correlation between performance in the high jump and the long jump.
  • D Being good at the high jump causes a competitor to be better at the long jump.
  • E There is no correlation or causation between high jump and long jump performance.

Q13:

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) 5.51 5.72 5.81 5.88 5.91 6.05 6.08 6.10 6.16 6.19 6.31 6.31 6.34 6.48 6.58
High Jump (m) 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 strong positive linear correlation between the long jump and high jump results.
  • BThere is a moderate negative 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 no real correlation between the long jump and high jump results.
  • EThere is a strong negative linear correlation between the long jump and high jump results.

Q14:

Which of the following correlation coefficients indicates the strongest correlation?

  • A 0 . 7 3
  • B0.62
  • C0
  • D 0 . 4 3

Q15:

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.

Q16:

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

  • A 1 and 0
  • B0 and 1
  • C 1 and 1
  • D0 and 100
  • E It depends on the scale of the data.

Q17:

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.

Q18:

Which of the following values could not represent a correlation coefficient?

  • A0.5
  • B0.9
  • C 0 . 5
  • D1.5

Q19:

Which of the following correlation coefficients suggests a negative causation between two variables?

  • A0.9
  • B0
  • C 0 . 8 4
  • DNo value of the correlation coefficient can suggest a causal relationship between two variables.
  • E0.31

Q20:

Determine whether the following statement is true or false: In order for the product-moment correlation coefficient for a data set to be equal to 1, the points must lie on a straight line with slope 1.

  • Atrue
  • Bfalse

Q21:

Using the information in the table, find the Pearson’s correlation coefficient and determine the type of correlation between the variables 𝑋 and 𝑌.

𝑋 6 11 14 4 8 10
𝑌 10 11 4 8 13 6
  • A 0 . 2 , inverse correlation
  • B 0 . 2 , direct correlation
  • C 0 . 3 1 4 3 , inverse correlation
  • D 0 . 3 1 4 3 , direct correlation

Q22:

Which of the following is not true about the correlation coefficient?

  • AA significant correlation indicates a causal relationship between two random variables.
  • BThe value of a correlation coefficient computed from a sample always lies between 1 and +1.
  • CWhen a sample correlation is significant, the null hypothesis of nonlinear association can be rejected.
  • DThe correlation coefficient is also known as Pearson’s 𝑟, named after its inventor Karl Pearson.

Q23:

Which of the following is the most appropriate interpretation of a product-moment correlation coefficient of 0.108?

  • Ano significant correlation
  • Ba moderate positive linear correlation
  • Ca strong negative linear correlation
  • Da strong positive linear correlation
  • Ea moderate negative linear correlation

Q24:

Determine whether the following statement is true or false: In order for the product-moment correlation coefficient for a data set to be equal to 1, the points must lie on a straight line with slope 1.

  • A false
  • B true

Q25:

Which of the following is the most appropriate interpretation of a product-moment correlation coefficient of 0.5?

  • A a strong negative linear correlation
  • B a moderate negative linear correlation
  • C a strong positive linear correlation
  • D no correlation
  • E a moderate positive linear correlation

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