Resolved: Contradictory situations in Q2 and Q5
From Q2, we find that the Marketing Expenditure is statistically significant as an independent variable. However, in Q5, when we combine Marketing expenditure with other independent variables, it becomes insignificant to the extent that we need to drop it to estimate the dependent variable for a test value. This seems like a contradiction: a statistically significant variable when taken alone becomes statistically insignificant and needs to be dropped when combined with other variables. Can you please explain this situation? Or am I making some misunderstanding?
Hello Dhaivat!
Thanks for reaching out!
That's is a great observation and question.
The significance of the Marketing Expenditure variable in simple linear regression compared to its apparent insignificance in multiple linear regression, when more factors are included, can be attributed to a common occurrence in regression analysis known as multicollinearity.
This happens when multiple predictors are correlated with each other. This correlation between predictors makes it challenging to isolate the unique contribution of each variable to the dependent variable, potentially diminishing the apparent significance of individual predictors, like Marketing Expenditure in this case.
Your observation does not necessarily indicate a contradiction but rather reflects the complexity of relationships among variables in regression models. A variable significant in a simple linear regression may not hold its significance in a multiple regression model due to the interplay with other variables, multicollinearity, and the redistribution of explained variance.
It's crucial in statistical modeling to understand that the role and significance of a predictor cannot be universally determined in isolation. They must be considered within the specific context of the model and alongside other variables. This understanding is fundamental when building, interpreting, and refining regression models to ensure accurate and meaningful insights.
Hope this helps!
Best,
The 365 Team