IM Alg1.3.8 Lesson: Using the Correlation Coefficient
Match the variables to the scatter plot you think they best fit. Be prepared to explain your reasoning.
Priya takes note of the distance the car drives and the time it takes to get to the destination for many trips.
Which of these factors (including distance) most likely has the most consistent influence for all the car trips? Explain your reasoning.
Use technology to create a scatter plot of the data and add the best fit line to the graph.
What do the slope and -intercept for the line of best fit mean in this situation?
Use the applet to find the correlation coefficient for this data. Based on the value, how would you describe the strength of the linear relationship?
How long do you think it would take Priya to make a trip of 90 miles if the linear relationship continues? If she drives 90 miles, do you think the prediction you made will be close to the actual value? Explain your reasoning.
For each situation, describe the relationship between the variables, based on the correlation coefficient.
Make sure to mention whether there is a strong relationship or not as well as whether it is a positive relationship or negative relationship.
Number of steps taken per day and number of kilometers walked per day.
Temperature of a rubber band and distance the rubber band can stretch.
Car weight and distance traveled using a full tank of gas.
Average fat intake per citizen of a country and average cancer rate of a country.
Score on science exam and number of words written on the essay question.
Average time spent listening to music per day and average time spent watching TV per day.
A biologist is trying to determine if a group of dolphins is a new species of dolphin or if it is a new group of individuals within the same species of dolphin.
The biologist measures the width (in millimeters) of the largest part of the skull, zygomatic width, and the length (in millimeters) of the snout, rostral length, of 10 dolphins from the same group of individuals.
The data appears to be linear and the equation of the line of best fit is and the -value is 0.201.
Compare the new equation of the line of best fit with the original. What impact did changing one data point have on the slope, -intercept, and correlation coefficient on the line of best fit?
Why do you think that weak positive association became a moderately strong association? Explain your reasoning.
How does changing each point’s -value impact the correlation coefficient?
Can you change two values to get the correlation coefficient closer to 1? Use data to support your answer.
By leaving , can you change a value to get the relationship to change from a positive one to a negative one? Use data to support or refute your answer.