Scenario 1: the mean intercept is positive and the mean slope is negative. Option a) the correlation between the mean intercept and mean slope of the outcome is positive. Does this indicate that those with higher levels of the intercept decline less? Option b) the correlation between the mean intercept and mean slope of the outcome is negative. Does this indicate that those with higher levels of the intercept decline more?
Scenario 2: the mean intercept is positive and the mean slope is positive. Option a) the correlation between the intercept and slope of the outcome is positive. Does this indicate that those with higher levels of the intercept increase more? Option b) the correlation between the intercept and slope of the outcome is negative. Does this indicate that those with higher levels of the intercept increase less?
Would the above interpretations apply similarly when I look at: 1) The correlation between the mean intercept of an outcome and the mean slope of the same outcome 2) The effect of the mean intercept of one outcome on the mean slope of another outcome 3) The effect of a baseline covariate on the slope of an outcome 4) How does the interpretation of a significant association between intercept and slope change when the mean slope is not significant?
I have a parallel model for both cognition (COG) and mobility limitations (ADL) and I estimate the coefficients between the slope factors. The slope of COG is negative but the slope for ADL is positive. I run into some difficulties in the interpretations. Consider these two cases:
Case 1: Slope of COG (-) on Slope of ADL (+). The coefficient is negative (-). Does this mean an increase in ADL result in a greater/greater decline in COG?
Case 2: Slope of ADL (+) on Slope of COG (-). The coefficient is negative (-). How can I interpret this result (ignoring the theoretical justification issue)?
I think case 1 and 2 should produce similar interpretations, but how could I interpret for case 2?
Also please consider the case below:
Case 3: Both the slopes of A and B were negative (-); the coefficient of B on A was positive (+). Does this mean a decrease in A result a faster/greater decrease in B?
I have reviewed many posts related to interpretation but still feel confused. Thank you so much (and thanks for the clear explanation above)!
The simple and general way to look at this is that you have x influencing y and you simply play out what happens to y for different x values given the sign of the regression coefficient. So for instance, in case 1, you have y=slope of COG and x=slope of ADL and the regression coefficient is negative. So when the x value increases, the y value goes down. Simple as that. The x value increases means that the slope of ADL goes up (increase in ADL). So the answer for Case 1 is Yes.
I'm also somewhat confused by the interpretation of 'Slope ON Intercept'. In my case intercept = a positive significant intercept; Slope = a negative significant slope. The regression coefficient is negative and significant.
Am I right in interpreting this by stating that higher intercepts predict greater negative/downward change in Y?