# statistics

posted by Jannel

Data on number of days of work missed and annual salary increase for a company's employees show that in general exployees who missed more days of work during the year received smaller raises than those who missed fewer days. A detailed analysis showed that number of days missed explained 74% of the variation in salary increases. What is the correlation between the number of days missed and salary increase?

1. bobpursley

I wonder what "explained" means.

If "explained" means the right thing, the correlation is .74

2. MathGuru

Coefficient of Determination is explained variation divided by total variation (or more simply, the correlation coefficient squared). To find the correlation coefficient, take the square root of .74 for your answer. The Coefficient of Determination shows the strength of the relationship between two variables. The ratio of explained variance to total variance represents the proportion of variability that is shared by the two variables. The Coefficient of Determination can be used to examine the usefulness of a regression line because it looks at the strength of the linear relationship.

3. MathGuru

One other comment:
Explained variation in this case is the variation in Y values that is explained by X values; unexplained variation is variation in Y values that cannot be explained by X values. Total variation is explained values plus unexplained values.

I hope this will help.

4. Jannel

I tried those answers and it didn't work.
=(

5. Jannel

I messed around the numbers and I sqrt .74 and added a negative sign to it and got it right. How do you know if it's a negative correlation?

6. MathGuru

Here's one way that might help you determine positive and negative correlations. With positive correlations, when one thing goes up, the other thing goes up. With negative correlations, when one thing goes up, the other goes down. With no correlation, there is no relationship between the two things.

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