In social sciences, we usually do not calculate bivariate models since cause-effect relationships in social phenomena are never bivariate. The previous model was just for easier access.
Now, we expand the model and calculate a multivariate linear regression. We want to include the variable trstlgl in the model. What effect do we theoretically expect from the variable trstlgl?
cor(
pss$trstlgl,
pss$stfdem,
method = "pearson",
use = "complete.obs"
)How do we interpret the result?
\(\Rightarrow\) The correlation value between trstlgl and stfdem indicates a negative correlation, but it is close to \(0\), suggesting that there is no relationship between the two variables.
We expand the model by adding the variable trstlgl.
We simply implement this in the lm() function:
olsModel2 <- lm(
stfdem ~ 1 + stfeco + trstlgl,
data = pss
)
summary(olsModel2)##
## Call:
## lm(formula = stfdem ~ 1 + stfeco + trstlgl, data = pss)
##
## Residuals:
## Min 1Q Median 3Q Max
## -5.7076 -1.0868 0.0396 1.1660 5.8289
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 0.67658 0.09318 7.261 4.44e-13 ***
## stfeco 0.87361 0.01355 64.468 < 2e-16 ***
## trstlgl -0.04212 0.01319 -3.194 0.00141 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.732 on 4890 degrees of freedom
## (107 observations deleted due to missingness)
## Multiple R-squared: 0.4598, Adjusted R-squared: 0.4596
## F-statistic: 2081 on 2 and 4890 DF, p-value: < 2.2e-16
How do we interpret the result? Write a few lines in your script!
The model can explain (45.96 %) of the variance in stfdem. With each increase in stfeco (satisfaction with economic performance), stfdem increases by (0.87361) points. With each increase in trust in the legal system (trstlgl), satisfaction with democracy decreases by (-0.04212). Both effects are significant ((p<0.05)).
So, you can now also calculate multivariate models and know how to interpret them!