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Analyzing a Linear Correlation between Two Variables

Question: Construct a scatter-plot, find the value of the linear correlation coefficient r, and find the critical values of r, using alpha = 0.05. Determine whether there is sufficient evidence to support a claim of a linear correlation between the two variables.

Scenario: Crickets and temperature
One classic application of correlation involves the association between the temperature and the number of times a cricket chirps in a minute. Listed below are the numbers of chirps in 1 minute and the corresponding temperatures in degree F. Is there a linear correlation between the number of chirps in 1 minute and the temperature?
- chirps in 1 min: 882, 1188, 1104, 864, 1200, 1032, 960, 900
- temperature (degree F) 69.7, 93.3, 84.3, 76.3, 88.6, 82.6, 71.6, 79.6

Solution Preview

Hi, please find the solution attached. I hope it will help you to understand the topic.

Solution:

Correlation coefficient is given as

chirps in 1 min temperature (degree F)
chirps in 1 min 1
temperature (degree F) 0.873679 1

Here we want to ...

Solution Summary

The expert analyzes a linear correlation between two variables. Sufficient evidence to support a claim of a linear correlation between the two variables are determined.

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