How to run a regression with a single explanatory variable and multiple dependent variables?

Question

I want to use a single explanatory variable in a data frame to explain changes in a number of other variables. The data frame looks something like:

df: 
explanatory_var dep_var_1 dep_var_2 dep_var_3
1               1.05      1.75      1.98
7               3.8       2.1       9.5
4.5             2         1.9       4

in pseudo code, I want to:

fit_df$coefficient <- lm((dep_var_1, dep_var_2, dep_var_3) ~ explanatory_variable, na.action = na.exclude)$coefficient
fit_df$intercept <- lm((dep_var_1, dep_var_2, dep_var_3) ~ explanatory_variable, na.action = na.exclude)$intercept
fit_df$coefficient_significance_code <- lm((dep_var_1, dep_var_2, dep_var_3) ~ explanatory_variable, na.action = na.exclude)$coefficient_significance_code
fit_df$intercept_significance_code <- lm((dep_var_1, dep_var_2, dep_var_3) ~ explanatory_variable, na.action = na.exclude)$intercept_significance_code

so that I end up with something like (data totally made up, doesn't fit the above, just an example)

fit_df: 
variable        coefficient intercept coefficient_significance_code intercept_significance_code 
dep_var_1       .35         0.5       ***                           ***
dep_var_2       .5          0.75      ***                           ***
dep_var_3       .43         1.0       ***                           ***

I have what I believe to be the opposite of this question: Using R's lm on a dataframe with a list of predictors

The answer seems like it is probably related to this: Repeat regression with varying dependent variable , but I am not creating my data frame, nor am I looking for an ls mean.

Answer 1

if you are using a single explanatory variable to explain changes in multiple dependent variables, a manova might be more appropriate for the task.

Using your data, it might go something like this:

exp_var <- c(1, 7, 4.5)
dep_var_1 <- c(1.05, 3.8, 2)
dep_var_2 <- c(1.75, 2.1, 1.9)
dep_var_3 <- c(1.98, 9.5, 4)
df <- data.frame(exp_var, dep_var_1, dep_var_2, dep_var_3)

model <- manova(cbind(dep_var_1,dep_var_2,dep_var_3) ~ exp_var, data = df)
summary(model)

By the way, there is not enough observations to run that code and it will result in an error. I hope that your dataset has plenty of observations. Hope this helps!