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What is regression coefficient and correlation coefficient?
The strength of the linear relationship between the two variables in the regression equation is the correlation coefficient, r, and is always a value between -1 and 1, inclusive. The regression coefficient is the slope of the line of the regression equation.
What is the relationship between correlation coefficient and linear regreassion?
A correlation coefficient is a value between -1 and 1 that shows how close of a good fit the regression line is. For example a regular line has a correlation coefficient of 1. A regression is a best fit and therefore has a correlation coefficient close to one. the closer to one the more accurate the line is to a non regression line.
What are the properties of correlation?
The correlation coefficient is symmetrical with respect to X and Y i.e.The correlation coefficient is the geometric mean of the two regression coefficients. or .The correlation coefficient lies between -1 and 1. i.e. .
How do you interpret coefficient of binary variable in linear regression?
This is my best shot. I've been trying to find this answer since I'm doing regressions right now. Let's say you have a dummy variable "male" where 1 = male, 2 = female. You regress: toads_owned = c(1) + c(2)*male You get the result: MALE: Coefficient: 2 T-test: 3.1 toads_owned = c(1) + 2*male So now, I think that means that if you are a male, you are likely to own 2 more toads on average than if you were a female. The coefficient on a dummy variable simply says how different you are from the base group (the group that equals 0) if you equal 1.
What can you conclude if the global test of regression does not reject the null hypothesis?
You can conclude that there is not enough evidence to reject the null hypothesis. Or that your model was incorrectly specified. Consider the exact equation y = x2. A regression of y against x (for -a < x < a) will give a regression coefficient of 0. Not because there is no relationship between y and x but because the relationship is not linear: the model is wrong! Do a regression of y against x2 and you will get a perfect regression!
