Respuesta :
Answer:
For this case the strongest linear association is given by the greatest correlation coeffcient in absolute value from the list provided. We have:
[tex] |r_3|>|r_2| > |r_4| > |r_1|[/tex]
So on this case we can conclude that the strongest linear association with number of wins is for runs allowed.
Step-by-step explanation:
Previous concepts
The correlation coefficient is a "statistical measure that calculates the strength of the relationship between the relative movements of two variables". It's denoted by r and its always between -1 and 1.
And in order to calculate the correlation coefficient we can use this formula:
[tex]r=\frac{n(\sum xy)-(\sum x)(\sum y)}{\sqrt{[n\sum x^2 -(\sum x)^2][n\sum y^2 -(\sum y)^2]}}[/tex]
Solution to the problem
For this case we have a list of correlation coefficients given:
[tex] r_1 = 0.51[/tex] represent the correlation between number of wins and shutouts
[tex] r_2 = 0.61[/tex] represent the correlation between number of wins and hits made
[tex] r_3 = -0.7[/tex] represent the correlation between number of wins and runs allowed
[tex] r_4 = -0.56[/tex] represent the correlation between number of wins and homeruns allowed
When we analyze linear association we are interested just in the absolute value for r since if r is near to +1 we have positive linear association but on the case that r is near to -1 we have an strong linear association but inversely proportional.
For this case the strongest linear association is given by the greatest correlation coeffcient in absolute value from the list provided. We have:
[tex] |r_3|>|r_2| > |r_4| > |r_1|[/tex]
So on this case we can conclude that the strongest linear association with number of wins is for runs allowed.
