Question

In a multilinear regression, state the reason why an independent variable may be found to be statistically insignificant, while in fact there is a clear correlation between that independent variable and the dependent variable?

Answer 1

In multilinear regression, an independent variable may be

found statistically insignificant, but it may happen that the

correlation between the independent variable and the

dependent variable is high. It is because of spurious

correlation. The dependent variable may behave similarly

as the independent variable but the independent variable

may not be able to capture the variation in dependent

variable.

Just for example if we want to predict the computer sales

and we include production of paddy as independent

variable, then the independent variable will not be

significant but there is a high correlation between these

two variables. It is because of the fact that due to

technological improvement both production of paddy and

computer sales improved over the years. So, they are highly

correlated.