Hi,
I am supposed to be running a multiple linear regressions to test my hypotheses. However, when first testing the assumptions that should be met before performing a linear regression, it turns out my data is extremely random. Linear relationships cannot be assumed, as can be seen in the scatterplots of these relationships (in the attachment both on individual level and country level).
Anyone know how I can make this data linear? Or is there no way to fix this problem and perform a multiple linear regression? Thanks!
M.
First, the "linear" in "linear regression" means linear in the parameters, not linear in the variables. You can estimate quadratic models with linear regression--you just square the predictor variable to make a proxy for the squared predictor and then continue with linear regression--Y is still a linear sum of the predictors.
Your data looks somewhat like a quadratic, with the slope first going down and then going back up. That suggests a quadratic model with negative linear slope and positive quadratic slope.
If the relationship is monotonic (only increasing or only descreasing) but not a straight line, you can use the Mosteller-Tukey "bulging rule" to guide you (see the atached graphic). You see the circle, with 4 quadrants. Find the curve that looks something like your data, and that tells you the kind of transformation that might linearize your data--taking Y to a higher or lower power, or taking X to a higher or lower power. Lower powers include the log, the square root, and negative exponentials.
First, the "linear" in "linear regression" means linear in the parameters, not linear in the variables. You can estimate quadratic models with linear regression--you just square the predictor variable to make a proxy for the squared predictor and then continue with linear regression--Y is still a linear sum of the predictors.
Your data looks somewhat like a quadratic, with the slope first going down and then going back up. That suggests a quadratic model with negative linear slope and positive quadratic slope.
If the relationship is monotonic (only increasing or only descreasing) but not a straight line, you can use the Mosteller-Tukey "bulging rule" to guide you (see the atached graphic). You see the circle, with 4 quadrants. Find the curve that looks something like your data, and that tells you the kind of transformation that might linearize your data--taking Y to a higher or lower power, or taking X to a higher or lower power. Lower powers include the log, the square root, and negative exponentials.
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