# Understanding multiple regression analysis results

#### psyabbey

##### New Member
Hi

I have conducted 2 Two separate Multiple Linear Regression Model test the relationship between the outcome variables, which was self-esteem and depression, with the predictor variables being; Instagram Intensity, social comparison orientation (SCO).

My results are as followed:

The first multiple linear regression was carried out to investigate whether Instagram Intensity score, and SCO could significantly predict participants self-esteem scores. It yielded a significant model that accounted for a larger proportion of the variance in the self-esteem score F (3,49) = 9.78, MSE = 113.78, p < .05, R² = .38. The results of the regression indicated that the model explained 39.8% of the variance. Whilst SCO contributed significantly to the model (b = - 2.195, p < .05) and was reliable, Instagram usage did not (b = - 0.09, p > .05). Here, as SCO increases self-esteem decreases. The interaction between SCO and Instagram usage was not significant.

The second multiple regression was carried out to investigate whether Instagram usage score, and SCO could significantly predict participants depression scores. It generated a significant model that accounted for a larger proportion of the variance in the depression scores F (3,49) = 6.04, MSE = 1228.3, p < .05, R² = 27%. The results of the regression indicated that the model explained 27% of the variance. Whilst SCO contributed significantly to the model (b = 1.25, p < .05) and was reliable, Instagram usage did not (b = .010, p > .05). Here, as social comparison increases, depression increases. The interaction between SCO and Instagram usage was significant (p <.05). This means that the regression model is statistically significant and a good predictor of the depression scores.

Essentially what are these both showing?
Any help would be much appreciated.

#### Miner

##### TS Contributor
Are you asking us to interpret the implications of these results or explain the statistical aspects behind the numbers? On the surface, it passes the common sense test. Having an undue fascination and comparing oneself to other people's pictures on Instagram could negatively impact self esteem and increase depression. It makes more sense than some wild claims I've seen. On the statistical end, The lower R^2 values may mean a number of things. This could be due to variation in the measurement process, variation in the subjects and latent variables that were not included in this analysis. The interaction will be easier to interpret if you plot it. It means that the Instagram Usage Score changes the slope of the regression line for SCO and Depression Score.

#### noetsi

##### Fortran must die
I am not sure that R square is a great measure of how important a model is. The tendency these days is to go with something AIC or chi square test for nested models. When you increase the variables in the model R square always will go up.

#### psyabbey

##### New Member
Are you asking us to interpret the implications of these results or explain the statistical aspects behind the numbers? On the surface, it passes the common sense test. Having an undue fascination and comparing oneself to other people's pictures on Instagram could negatively impact self esteem and increase depression. It makes more sense than some wild claims I've seen. On the statistical end, The lower R^2 values may mean a number of things. This could be due to variation in the measurement process, variation in the subjects and latent variables that were not included in this analysis. The interaction will be easier to interpret if you plot it. It means that the Instagram Usage Score changes the slope of the regression line for SCO and Depression Score.
Brilliant thank you! I have manged to plot the data and it is clear to interpret. Really glad the data makes sense, I need it clarifying.

#### psyabbey

##### New Member
I am not sure that R square is a great measure of how important a model is. The tendency these days is to go with something AIC or chi square test for nested models. When you increase the variables in the model R square always will go up.
Thank you. I had not consider this, Chi squared test seems appropriate.

#### psyabbey

##### New Member
Are you asking us to interpret the implications of these results or explain the statistical aspects behind the numbers? On the surface, it passes the common sense test. Having an undue fascination and comparing oneself to other people's pictures on Instagram could negatively impact self esteem and increase depression. It makes more sense than some wild claims I've seen. On the statistical end, The lower R^2 values may mean a number of things. This could be due to variation in the measurement process, variation in the subjects and latent variables that were not included in this analysis. The interaction will be easier to interpret if you plot it. It means that the Instagram Usage Score changes the slope of the regression line for SCO and Depression Score.
Could you interpret the implications of these results and explain the statistical aspects behind the numbers?
Many Thanks!

#### noetsi

##### Fortran must die
Thank you. I had not consider this, Chi squared test seems appropriate.
If you use a chi square test, and I am not sure which one you mean, the models have to be nested. Or you should use AIC, BIC etc.