Correlation Syntax for R

Question

Very basic question, it's my first time writing syntax in R. Trying to write basic correlation syntax. Hypothesis is as follows: X1 (Predictor variable) and X2 (latent predictor variable) will be positively associated with Y (outcome variable), over and above X3 (latent predictor variable). How can I write this in R?

Answer 1

Not sure what your statistics chops are, but pure the correlation as measured by the r-squared value will strictly increase with added variables to your model. So, if these variables are stored in data frame df,

model_full <- lm(Y ~ X1 + X2 + X3, data = df)

fits the full model. Use summary(model_full) to view summary statistics of the model.

model_reduced <- lm(Y ~ X3, data = df)

fits the reduced model. Here's where the more complicated stuff comes in. To test the value of X1 and X2, you probably want an F-test to test whether the coefficients on X1 and X2 are jointly statistically significantly different from zero (this is how I interpret 'above and beyond X3'). To compute that test, use

lmtest::waldtest(model_full, model_reduced, test = "F")

Hope this helps!