This is my worst subject so I’m trying to spend some time on it. I NEED HELP!!!
I am very confused about the relationship betwene the slope coefficient and the correlation coefficient. Intuitively, it seems to me that they should be the same thing but there is some difference that is not apparent to me. Why are the formulas for them a little different? One has the denominator as the st dev of x times the st dev of y, the other has the denominator as the st dev of x times the st dev of x (i.e. the variance of x).
Is the correlation the same thing as r? I think that the slope is the regression sum of sqares and the r squared is the percent of the regression sum of squares to the total squared differences between y values and estimated y values.
Also, why are there 3 different ways or formulas to test the signifincance of the correlation coefficient. Are there just 3 different ways to do the same thing and they could expect us to do it using any of these 3 methods depending how they ask the question, hence there are 3 different LOS’s asking us to essentiall do the same thing?
Method one from LOS 11.c involves the following formula fot the t calcualtion: t = r (sq root of (n-k-1))/ sq root of (1-r squared)
Method 2 from LOS 11.f involves calculating a confidence interval for a regression coefficient and determining whether the confidence interval includes zero or not.
Method 3 from LOS 11.g that uses the same info from method 2
I understand how to do each calculation in each of these methods but I don’t understand the relationship or should I say the difference between what these 3 methods are telling us. I’m not sure I would be able to distinguish one method from the other and would not know how to answer a question.
The slope coefficient is just what the name says: the slope of the regression line. The correlation coefficient is an indication of how closely the data fit that regression line. Although the formulae are similar, the ideas are quite different; they’re definitely not the same thing.
Yes. (Technically, r is a sample correlation and ρ is a population correlation, but the values are the same.)
Furthermore,
R² = _r_² (= ρ²).
There aren’t. Again, the correlation coefficient isn’t the same as the slope coefficient. The LOSs are sloppy here: they use the term “regression coefficient” when they mean “slope coefficient”; the slope coefficient and the intercept are both regression coefficients.
Method 1 pertains to regression coefficients (r or ρ). Methods 2 and 3 pertain to slopes.