Hi all, I recently created a regressor using lm() to establish the linear regression of a dependent variable over an independent one using this code:

regressor = lm(formula = Dependent var ~ Independent var, data = dataset)

After running its summary to evaluate significance and coefficient correlation I was quite surprised to find these results:

summary(regressor)

Pvalue: < 2e-16 ***

Multiple R-squared: 0.5338

Adjusted R-squared: 0.5328

In my mind a high statistical significance is tied to a high R squared close to 1, but this seems not to be the case.

Plotting the data indeed I see dots all over the place, although there is a weak tendency towards positive regression...

Could anyone help me to interpret these results and the validity of this model?

Thanks

Alex

regressor = lm(formula = Dependent var ~ Independent var, data = dataset)

After running its summary to evaluate significance and coefficient correlation I was quite surprised to find these results:

summary(regressor)

Pvalue: < 2e-16 ***

Multiple R-squared: 0.5338

Adjusted R-squared: 0.5328

In my mind a high statistical significance is tied to a high R squared close to 1, but this seems not to be the case.

Plotting the data indeed I see dots all over the place, although there is a weak tendency towards positive regression...

Could anyone help me to interpret these results and the validity of this model?

Thanks

Alex

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