Is the regression line steeper than the SD line?

The SD line shows how x and y are varying and this can give a more or less steep or flat line depending on the ratio σyσx. The regression line will be always with a smaller slope than the SD line(You might relate this to regression to the mean). By how much smaller will depend on the correlation.

Is the slope of the regression line positive or negative?

In general, straight lines have slopes that are positive, negative, or zero. If we were to examine our least-square regression lines and compare the corresponding values of r, we would notice that every time our data has a negative correlation coefficient, the slope of the regression line is negative.

Is regression of X on Y the same as Y on X?

The correlation coefficient, r, is the slope of the regression line when both variables have been standardized first. The cloud of data points will now be centered on the origin, and the slope would be the same whether you regressed y onto x, or x onto y (but note the comment by @DilipSarwate below).

Does the regression line always pass through a point?

The least-squares regression line always passes through the point (x, y). 3. The square of the correlation, r2, is the fraction of the variation in the values of y that is explained by the least- squares regression of y on x.

Why does the regression line always go through the mean?

If there is no relationship between X and Y, the best guess for all values of X is the mean of Y. If there is a relationship (b is not zero), the best guess for the mean of X is still the mean of Y, and as X departs from the mean, so does Y. At any rate, the regression line always passes through the means of X and Y.

When the slope of the regression equation is negative?

If the slope is negative, y decreases as x increases and the function runs downhill. If the slope is zero, y does not change, thus is constant—a horizontal line.

When regression line passes through the origin then regression coefficient is zero?

Regression through the origin is when you force the intercept of a regression model to equal zero. It’s also known as fitting a model without an intercept (e.g., the intercept-free linear model y=bx is equivalent to the model y=a+bx with a=0).

How the regression line always passes through?

At any rate, the regression line always passes through the means of X and Y. This means that, regardless of the value of the slope, when X is at its mean, so is Y.