Question

In the following case, determine and explain if we can interpret ?? as the causal effect of the relevant ? variable on ?.

A random sample of students at a University are surveyed and data is collected on their high-school score and whether they have enrolled in any mathematics course during their time at the University. The following model is estimated

???ℎ??????? = ?0 + ?1????? + ?2??? + ?

Here, the variable ???ℎ??????? captures whether the student enrolled in any mathematics course in their time at the University or not, ????? is their high-school score and ??? is the student’s age in years.

Answer 1

???ℎ??????? = ?0 + ?1????? + ?2??? + ?

variable ???ℎ??????? captures whether the student enrolled in any mathematics course in their time at the University or not, ????? is their high-school score and ??? is the student’s age in years.

?? represents that when score changes by 1 unit, the average predicted value of mathematics changes by ?? units.

if ?? is positive then the relation between x and y variable is direct

if ?? is negative then the relation between x and y variable is indirect

if ??=0 then x variable has no effect on y variable