Given two regression coefficients are 0.45 and 0.54 the coefficient of determination is

Sometimes, you may want to see how closely two variables relate to one another. In statistics, we call the correlation coefficient r, and it measures the strength and direction of a linear relationship between two variables on a scatterplot. The value of r is always between +1 and –1. To interpret its value, see which of the following values your correlation r is closest to:

Exactly –1. A perfect downhill (negative) linear relationship
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–0.70. A strong downhill (negative) linear relationship
–0.50. A moderate downhill (negative) relationship
–0.30. A weak downhill (negative) linear relationship
0. No linear relationship
+0.30. A weak uphill (positive) linear relationship
+0.50. A moderate uphill (positive) relationship
+0.70. A strong uphill (positive) linear relationship
Exactly +1. A perfect uphill (positive) linear relationship

If the scatterplot doesn’t show that there’s at least somewhat of a linear relationship, the correlation doesn’t mean much. Why measure the amount of linear relationship if there isn’t much of one?

However, you can think of this idea of no linear relationship in two ways: 1) If no relationship at all exists, calculating the correlation doesn’t make sense because correlation only applies to linear relationships, and 2) If a strong relationship exists but it’s not linear, the correlation may be misleading, because in some cases a strong curved relationship exists. That’s why it’s critical to check out the scatterplot first.

Scatterplots with correlations of a) +1.00; b) –0.50; c) +0.85; and d) +0.15

The above figure shows examples of what various correlations look like, in terms of the strength and direction of the relationship. Figure (a) shows a correlation of nearly +1, Figure (b) shows a correlation of –0.50, Figure (c) shows a correlation of +0.85, and Figure (d) shows a correlation of +0.15.

Comparing Figures (a) and (c), you see Figure (a) is nearly a perfect uphill straight line, and Figure (c) shows a very strong uphill linear pattern (but not as strong as Figure (a)). Figure (b) is going downhill, but the points are somewhat scattered in a wider band, showing a linear relationship is present, but not as strong as in Figures (a) and (c). Figure (d) doesn’t show much of anything happening (and it shouldn’t, since its correlation is very close to 0).

Many folks make the mistake of thinking that a correlation of –1 is a bad thing, indicating no relationship. Just the opposite is true! A correlation of –1 means the data are lined up in a perfect straight line, the strongest negative linear relationship you can get. The “–” (minus) sign just happens to indicate a negative relationship, a downhill line.

How close is close enough to –1 or +1 to indicate a strong enough linear relationship? Most statisticians like to see correlations beyond at least +0.5 or –0.5 before getting too excited about them. Don’t expect a correlation to always be 0.99 however; remember, these are real data, and real data aren’t perfect.

About This Article

This article is from the book:

Statistics For Dummies ,

About the book author:

Deborah J. Rumsey, PhD, is an Auxiliary Professor and Statistics Education Specialist at The Ohio State University. She is the author of Statistics For Dummies, Statistics II For Dummies, Statistics Workbook For Dummies, and Probability For Dummies.

This article can be found in the category:

Statistics ,

If two regression coefficients are -0.8 and -0.2, then the value of coefficient of correlation is

-0.16
-0.50
+0.40
-0.40

Answer (Detailed Solution Below)

Option 4 : -0.40

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The geometric mean between the two regression coefficients is equal to the correlation coefficient.

R = √(byx*bxy) = √(-0.8 * -0.2) = √0.16 = - 0.40

The '+' or '-' sign is given to the correlation coefficient based on the signs of the two regression coefficients.

Therefore, If the two regression coefficients are -0.8 and -0.2, then the value of the coefficient of correlation is - 0.40.

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What does a correlation coefficient of 0.45 mean?

We know that a correlation of 1 means the two variables are associated positively, whereas if the correlation coefficient is 0, then there is no correlation between two variables. Thus, a correlation of 0.45 means 45% of the variance in one variable, say x, is accounted for by the second variable, say y.

Is a correlation coefficient of 0.45 strong?

For example, with demographic data, we we generally consider correlations above 0.75 to be relatively strong; correlations between 0.45 and 0.75 are moderate, and those below 0.45 are considered weak.

What does a 0.5 coefficient of determination mean?

Understanding the Coefficient of Determination But a value of 0.20, for example, suggests that 20% of the dependent variable is predicted by the independent variable, while a value of 0.50 suggests that 50% of the dependent variable is predicted by the independent variable, and so forth.

What does a coefficient of determination r2 value of 0.4 indicate?

In finance, an R-Squared above 0.7 would generally be seen as showing a high level of correlation, whereas a measure below 0.4 would show a low correlation.