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When both the regression lines are then r 0?
If r = 0, then the two lines will be the respective means of Y and X, and the regression lines will be the same as the major axes of the figure. For values of r between 0 and 1, there will be two regression lines that form an interior angle less than 90 degrees, as illustrated in the figure below.
When r =- 1 or 1 then the regression lines are?
The two lines of regression coincide i.e. become identical when r = –1 or 1 or in other words, there is a perfect negative or positive correlation between the two variables under discussion.
When the correlation coefficient r =+- 1 then the two regression lines are?
(1) If the correlation coefficient rxy=0, then the two lines of regression are parallel to each other.
How to test the equality of regression coefficients?
How do you test the equality of regression coefficients that are generated from two different regressions, estimated on two different samples? You must set up your data and regression model so that one model is nested in a more general model. For example, suppose you have two regressions,
When do regressions come from two different samples?
When the regressions come from two different samples, you can assume: V a r ( β 1 − β 2) = V a r ( β 1) + V a r ( β 2) which leads to the formula provided in another answer. But your question was precisely related to the case when c o v a r ( β 1, β 2) ≠ 0. In this case, seemingly unrelated equations seems the most general case.
When do regression lines shift up or down?
When the constant (y intercept) differs between regression equations, the regression lines are shifted up or down on the y-axis. The scatterplot below shows how the output for Condition B is consistently higher than Condition A for any given Input.
When to use hypothesis test in regression models?
By including a categorical variable in regression models, it’s simple to perform hypothesis tests to determine whether the differences between constants and coefficients are statistically significant. These tests are beneficial when you can see differences between models and you want to support your observations with p-values.