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If two variables are uncorrelated then regression lines are(a) Parallel(b) Perpendicular(c) Coincident(d) Inclined at 45 0

Question

If two variables are uncorrelated then regression lines are(a) Parallel(b) Perpendicular(c) Coincident(d) Inclined at 45 0

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Solution

The correct answer is (a) Parallel.

Here's why:

Correlation measures the strength and direction of the linear relationship between two variables. If two variables are uncorrelated, it means there is no linear relationship between them.

In the context of regression lines, if there is no relationship between the two variables, the regression line would be a flat line (i.e., a horizontal line), indicating no change in the dependent variable as the independent variable changes.

If you have two such variables and you draw regression lines for each, the lines would be parallel to each other because neither line indicates any change in the dependent variable as the independent variable changes.

So, if two variables are uncorrelated, their regression lines are parallel.

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