Checking interaction between one dependent continuous variable and two independent continuous variable

Question

I am trying to figure out if there is a way that we can perform some statistical test to check the interaction between two independent continuous variables and a dependent variable in R.

I have three variables course completion rate, interaction coefficient of participants, and sentiment scores. I want to check if there exists any relationship:

If the course completion rate depends on the interaction coefficient and sentiment scores.

I have checked for the normality of the variables, and they follow a normal distribution using a qq-plot.

I have done something like using anova:

model <- aov(completion_rate ~ eta * synergy_scores,
             data = eta_scores)

summary(model)

I get an output like:

                   Df Sum Sq Mean Sq F value Pr(>F)
eta                 1  0.064 0.06394   1.413  0.238
synergy_scores      1  0.065 0.06481   1.432  0.235
eta:synergy_scores  1  0.005 0.00512   0.113  0.737
Residuals          88  3.982 0.04525      

Is it the right way to compare two continuous variable like this?

Answer 1

ANOVA models the influence of categorical variables on a continuous dependent variable. In your case, (non)linear regression may be tried.

First, you can make a scatterplot to see if the relationship between the dependent variable and each individual independent variable is linear. If not, you may want to try to transform either variable so that the relationship become linear and then to run a linear regression.

The output you have shows that the influence of individual factors is not statistically significant, because no p-value is less than 0.05.