Worksheet: Linear Correlation

In this worksheet, we will practice dealing with linear correlation and distinguishing between different types of correlation.

Q1:

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

  • Aa positive linear correlation
  • Bno correlation
  • Ca negative linear correlation

Q2:

What type of correlation does this graph show?

  • Aa negative correlation
  • Ba positive correlation
  • Cno correlation

Q3:

Can we use the line of best fit to describe the trend in the data? Why?

  • AYes, because the data shows a linear trend.
  • BNo, because the data shows an exponential trend not a linear trend.

Q4:

The scattergraph shows the average gestation period, measured in days, against the average brain mass of an adult, measured in grams, for 13 species of mammals.

What type of correlation appears to exist between the gestation period and the brain mass?

  • Aa negative linear correlation
  • Ba positive linear correlation

What is the correct interpretation of this relationship?

  • AIn general, as the gestation period increases, the brain mass decreases.
  • BA greater brain mass leads to a longer gestation period.
  • CIn general, as the gestation period increases, so too does the brain mass.
  • DIn general, as the gestation period decreases, the brain mass increases.

Q5:

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

  • Ano correlation
  • Ba negative linear correlation
  • Ca positive linear correlation

Q6:

What type of linear correlation might exist between the mass loaded onto a spring and its extension?

  • Ano correlation
  • Ba negative correlation
  • Ca positive correlation

Q7:

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?

  • Anegative correlation
  • Bno correlation
  • Cpositive correlation

Q8:

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?

  • Anegative correlation
  • Bpositive correlation
  • Cno correlation

Q9:

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.

Q10:

What type of correlation does the graph show?

  • Anegative correlation
  • Bno correlation
  • Cpositive correlation

Q11:

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

  • AA negative linear correlation
  • BA positive linear correlation
  • CNo correlation

Q12:

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

  • Anegative correlation
  • Bno correlation
  • Cpositive correlation

Q13:

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 positive correlation
  • Ca negative correlation

Q14:

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

  • ANo correlation
  • BPositive correlation
  • CNegative correlation

Q15:

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

  • Aa positive correlation
  • Ba negative correlation
  • Cno correlation

Q16:

Does all bivariate data suggest a linear relationship?

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

Q17:

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
  • Bpositive correlation
  • Cnegative correlation

Q18:

Suppose variable 𝑥 is the number of hours you work, and variable 𝑦 is your salary. You suspect that the more hours you work, the higher your salary is. Does this follow a positive correlation, a negative correlation, or no correlation?

  • Apositive correlation
  • Bnegative correlation
  • Cno correlation

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