Lets say for a sample of data the correlation coefficient is zero. I know this means...

Lets say for a sample of data the correlation coefficient is zero. I know this means there is no linear relationship, and if you tried to fit the data by a least-squares then the slope would also be zero. But if you did this analysis, could you get a nonzero y-intercept? I think you could, but curious to see what other people think.

Expert Solution

A no linear relationship happens when we get a straight horizontal line parallel to the x axis. This line can extend to infinity on both sides and hence will cut the y axis at some point, and this point where the line cuts the y axis is called the y intercept (or the regression coefficient b0.)

Lets take a linear regression equation of the form = mx + c, where m is the slope and c is the y intercept

When m = 0, we get = c, which means for every value of x, we have the same value of , which gives us a straight line.

The only way of getting the y intercept at 0, is when the equation of the line is the x axis itself. This line would be = 0.

Other than this line, all other lines with slope = 0, will have a non zero y intercept.

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orchestra answered 2 years ago

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