Lesson: Linear Correlation Coefficient

In this lesson, we will learn how to calculate and use the correlation coefficient r to describe the strength and direction of a linear relationship.

Sample Question Videos

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Worksheet: Linear Correlation Coefficient • 25 Questions • 3 Videos

Q1:

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

Q2:

Which of the following correlation coefficients indicates the strongest correlation?

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?

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?

Q5:

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

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.

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

Q9:

Which of the following correlation coefficients indicates the weakest correlation?

Q10:

Which of the following correlation coefficients indicates the weakest correlation?

Q11:

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

Q12:

What type of correlation does the graph show?

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?

Q15:

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

Q16:

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

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?

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?

Q20:

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

Q21:

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

Q22:

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

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?

Q24:

Does all bivariate data suggest a linear relationship?

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?

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