Worksheet: Linear Correlation Coefficient

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

Q1:

The following scatterplot shows the heights and weights of 24 students in a class. Which of the following is true?

  • AThere is no correlation between height and weight.
  • BThe heavier you are, the shorter you are.
  • CThere is a negative correlation between height and weight.
  • DThe data has an outlier.

Q2:

Which of the following correlation coefficients indicates the strongest correlation?

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

Q3:

Suppose variable 𝑥 is the speed of a car and variable 𝑦 is the car’s travel time to its destination. You suspect that if the car decreases its speed, its travel time to the destination increases. Does this follow a positive correlation, negative correlation, or no correlation?

  • Ano correlation
  • Bpositive correlation
  • Cnegative correlation

Q4:

Suppose variable 𝑥 is the speed of a train and variable 𝑦 is the time for the train to get to the station. You suspect that the more the train increases its speed, the less time it takes to get to the station. Does this follow a positive correlation, negative correlation, or no correlation?

  • Ano correlation
  • Bpositive correlation
  • Cnegative correlation

Q5:

If the data points all line up on the line of best fit, what does this say about the data?

  • AThere is a very weak correlation between the variables.
  • BThere is no correlation at all between the variables.
  • CThere is a very strong correlation between the variables.

Q6:

Find the Pearson correlation coefficient and determine the type of the correlation of the variables 𝑋 and 𝑌 if Give your answer to four decimal places.

  • A − 0 . 0 9 9 0 , inverse correlation
  • B − 0 . 0 9 9 0 , direct correlation
  • C − 0 . 5 9 6 2 , direct correlation
  • D − 0 . 5 9 6 2 , inverse correlation

Q7:

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

Q8:

The table shows the marks that 10 students received in history and geography. Calculate the Pearson’s correlation coefficient and determine the type of correlation.

History 92 72 69 94 85 73 67 68 68 96
Geography 73 86 87 88 76 81 95 85 92 74
  • A − 0 . 0 7 0 5 , inverse correlation
  • B − 0 . 0 7 0 5 , direct correlation
  • C − 0 . 6 9 2 4 , direct correlation
  • D − 0 . 6 9 2 4 , inverse correlation

Q9:

Which of the following correlation coefficients indicates the weakest correlation?

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

Q10:

Which of the following correlation coefficients indicates the weakest correlation?

  • A − 0 . 4 9
  • B − 0 . 8 8
  • C0.77
  • D − 0 . 2 6

Q11:

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

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

Q12:

What type of correlation does the graph show?

  • Ano correlation
  • Bpositive correlation
  • Cnegative correlation

Q13:

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

Q14:

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

  • A0.37
  • B − 0 . 5 8
  • C0
  • D − 0 . 9 4
  • E0.78

Q15:

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

  • A0.37
  • B − 0 . 9 4
  • C0
  • D − 0 . 5 8
  • E0.78

Q16:

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

  • A − 0 . 9 4
  • B − 0 . 5 8
  • C0
  • D0.37
  • E0.78

Q17:

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?

Q18:

What type of correlation exists between the two variables in the shown scatterplot?

  • ANo correlation
  • BA positive linear correlation
  • CA negative linear correlation

Q19:

The following scatter diagram shows the scores of two tests for a class of 26 students. What type of correlation does the graph show?

  • Ano correlation
  • Bnegative correlation
  • Cpositive correlation

Q20:

The following scatterplot shows the heights and weights of 24 students in a class. What type of correlation does this graph show?

  • Ano correlation
  • Ba negative correlation
  • Ca positive correlation

Q21:

Why is it sometimes better to use a scatter plot than a list of the points?

  • A There is less data on the scatter plot than in a list of points.
  • B The data on a scatter plot is more accurate than a list of points.
  • C The two are equivalent and there is no difference between the two methods.
  • D The scatter plot gives a good sense of data trends and overall behaviour.

Q22:

What type of linear correlation might exist between the time a student takes to travel to school and the age of the student?

  • ANegative correlation
  • BPositive correlation
  • CNo correlation

Q23:

What type of linear correlation might exist between the number of hours spent on social media and the number of hours spent doing homework?

  • Ano correlation
  • Ba positive correlation
  • Ca negative correlation

Q24:

Does all bivariate data suggest a linear relationship?

  • AYes. Otherwise, drawing a scatter plot would not be possible.
  • BYes, that is what “bivariate” means.
  • CNo, because lines of best fit work for nonlinear relationships as well.
  • DNo, because some variables are not correlated linearly or at all.

Q25:

Suppose variable 𝑥 is the number of hours you spent studying, and variable 𝑦 is your grade in the final exam. You suspect that the more hours you spend studying, the higher your grade is. Does this follow a positive correlation, a negative correlation, or no correlation?

  • Ano correlation
  • Bnegative correlation
  • Cpositive correlation

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