Unlocking the full potential of your linear regression analysis starts with validating its suitability. Here’s a summary of how to validate assumptions before applying this model:
1️⃣ Linearity: The relationship between predictors (independent variables) and the response (dependent variable) should be linear. Think of a car traveling at a constant speed: the distance traveled increases proportionally with time.
2️⃣ Independence: Residuals (errors) must be independent of each other. Picture students taking an exam in separate rooms without communication. Each student's score is independent of the others.
3️⃣ Homoscedasticity vs. Heteroscedasticity: Residuals should have a constant spread across all levels of the independent variable. If the variability changes, like scores varying differently for easy versus hard exam questions, it indicates heteroscedasticity, which is problematic.
4️⃣ Normality of Residuals (Multivariate Normality): Residuals should follow a normal distribution, similar to the bell curve seen when rolling a fair die many times.
5️⃣ No Multicollinearity: Independent variables should not be highly correlated with each other. Imagine assessing the impact of both age and experience on salary: if they move together, it’s hard to distinguish their individual effects.
6️⃣ Measurement Error: Measurement errors can lead to unreliable predictions. It’s like weighing fruits on a scale that occasionally gives wrong readings.
The visualization originates from a recent post by @intelligentle__
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