1. ## Multiple Regression theory

Hey guys I'm not too good with the logic of multiple regression so I'd like some enlightenment on the following query.

I'm running a multiple regression on the following;

IV1: Protective factors
IV2: Risk factors
IV3: IAT score

DV: Number of Suicide attempts

Now my hypothesis is that each IV will contribute significantly to the change in R-squared.

BUT only the Risk factors and IAT score are positively correlated with the number of suicide attempts. Protective factors is actually negatively correlated.

So the question is, can I use the multiple regression to answer my hypothesis?

Intuitively I feel that if I include a negatively correlated IV it is not going to help me predict the DV at all. If I'm wrong could someone please give an explanation.

Much appreciated!

2. ## Re: Multiple Regression theory

Hi durantz, interesting question.

Now my hypothesis is that each IV will contribute significantly to the change in R-squared.
Is this your null hypothesis? How would you judge whether the change in R-Squared is significant or not? Drop of 2%, 5%? (Never seen hypothesis defined in terms of R-2).

The negative correlation makes sense, as if there are more protective factors (support from friends and family etc..)around the patient, the less likely they are to commit a suicide.
I think it would be wrong to exclude this as this is an important variable that you need to take into account.
As you've just 3 IV, I think you can use all of these 3 variables to perform a multiple regression and assess their significance in the presence of other variables in the model.

In any case, if you have more IV in the model, it should help in predicting better.

3. ## Re: Multiple Regression theory

Thanks for that ledzep.

To be specific I'm doing a hierarchical multiple regression.

In SPSS it calculates the F-ratio associated with the change in R-squared, thus telling me whether or not it is significant.

I will attach my results table for the regression if that helps. As you will see in both steps of the regression only risk factors has a significant standardised beta. From this results table I am going to conclude that only 'risk factors' contributes significantly to the prediction of number of suicide attempts.

So what you're saying is that it doesn't matter if you include positively and negatively correlated IVs in the regression? My intuitions just had me thinking you'd only want to include variables that are ALL positively correlated or ALL negatively correlated. But now that I think about it that seems wrong.

Edit: just noticed my table is mislabelled. It should be No. of previous suicide attempts.

4. ## Re: Multiple Regression theory

Now my hypothesis is that each IV will contribute significantly to the change in R-squared.
a) Each predictor is associated with number of suicide attemts (three univarite analyses).
b) the three predictors jointly can predict nimber of suicide attempts (model R² in multiple regression).
c) each predictor in the model independently contributes to the prediction (as can be seen by significant regression weights in the multiple regression).
Intuitively I feel that if I include a negatively correlated IV it is not going to help me predict the DV at all. If I'm wrong could someone please give an explanation.
Oops. What concept of correlation/negative correlation do you have in mind?
Negative correlation does not decrease prediction. Change "number of predictive factors"
(say, now numbers between 0 and 11) into "number of lacking protective factors" (say, how
many of 20 factors were lacking) then you'l have a positive correlation while conceptually
there hasn't been changed anything.

Kind regards

K.

5. ## Re: Multiple Regression theory

Thanks a lot Karabiner! Those hypotheses are very helpful.

I should be fine now.

6. ## Re: Multiple Regression theory

- Very often, if additional independent variables are included, R-2 will increase. Normally, I always look at the adjusted R-2 (in spss) to see whether an addidtional variable makes sense, because the adjusted R-2 accounts for the number of variables included.

- Second, R-2 measures how much of the variation in your dependent variable can be explained by your independent variables, so.. a significant negative correlation is actually good and will enhance R-2.

just to make things a bit more clear

7. ## Re: Multiple Regression theory

Originally Posted by Eyecatcher

- Very often, if additional independent variables are included, R-2 will increase.
And by "very often" they mean that it's actually impossible for R^2 to decrease when you add a predictor.

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