For a data set of chest sizes (distance around chest in inches) and weights (pounds) of twelve anesthetized bears that were measuredthe linear correlation coefficient is r = 0.442 Use the table available below to find the critical values of Based on a comparison of the linear correlation coefficient r and the critical values, what do you conclude about a linear correlation?
Number of pairs of data n:
4, 5,6,7,8,9,10,11,12
Critical Value of r: 0.950,0.878,0.811,0.754,0.707,0.666,0.632,0.602,0.576
(I forgot to add this)
To find the critical values based on the linear correlation coefficient (r) in the table, we need to know the sample size (n). Since the sample size is not provided in your question, we cannot determine the exact critical values from the table. However, I can provide you with an explanation of how to interpret the linear correlation coefficient r in relation to the critical values.
The linear correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. It ranges from -1 to +1. A positive value for r indicates a positive correlation (direct relationship), while a negative value indicates a negative correlation (inverse relationship). The closer r is to +1 or -1, the stronger the relationship. A value of r = 0 indicates no linear relationship.
To compare the linear correlation coefficient (r) with the critical values, we can use the following guidelines:
1. If the absolute value of r is less than the critical value, the correlation is not significant, and there may not be a linear relationship between the variables.
2. If the absolute value of r is greater than the critical value, the correlation is significant, and there is evidence of a linear relationship between the variables.
The critical values vary based on the sample size (n) and the desired significance level (α). Commonly used significance levels are 0.05 (5%) or 0.01 (1%).
For example, if the absolute value of r is greater than the critical value at a significance level of 0.05, we can conclude that there is a significant linear relationship between the variables.
Please provide the sample size (n) and the significance level (α), and I can help you determine the corresponding critical values from the table and draw a conclusion about the linear correlation.