Question

Given two sets of data, A and B.

i) Data set A has an r value of -.81 and data set B has an r value of .94 Describe the differences between the two data sets as completely as you can using the regression information we have learned.

ii) Which linear regression equation, the one for A or the one for B, would probably be a better predictor? Why?

Answer 1

Solution :-

i)

Data set A has r value ( Correlation Coefficient ) = -0.81 i.e Negative higher degree of correlation.

When two related variables move in opposite directions, their relationship is negative.

When the coefficient of correlation (r) is less than 0, it is negative. When r is -1.0, there is a perfect negative correlation

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Data set B has r value ( Correlation Coefficient ) = 0.94 i.e Positive higher degree of correlation.

When two related variables move in the same direction, their relationship is positive.

This correlation is measured by the coefficient of correlation (r).

When r is greater than 0, it is positive. When r is +1.0, there is a perfect positive correlation.

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ii )

In this case Linear regression equation ( B ), r = 0.94 is better predicter than ( A ) , r = - 0.81 .

Because --

The correlation coefficient, r, can range from -1 to +1. When r = +1, there is a perfect positive correlation between two variables. When r = -1, there is a perfect negative correlation between two variables. When r = 0, there is no correlation between the variables. In reality, it's very rare to find r values of +1 or -1; rather, we see r values somewhere between these two extremes. For example, if we determined that two variables had an r value of 0.94, for all practical purposes, that would indicate a very strong, but not perfect, positive correlation between the two variables. Similarly, an r value of -0.81 would indicate a very strong, but not perfect, negative correlation between the two variables.

Condition for correlation are :-

r = 0 - No Correlation

r = 0 to  +/- ( 0.25 ) -- Lower degree of Correlation.

r = +/- 0.25 to +/- 0.75 -- Moderate degree of Correlation.

r = +/- 0.75 to +/- 0.99 -- Higher degree of Correlation.

r = - 1 = Perfect Negative Correlation.

r = +1 = Perfect Positive  Correlation.