Which assumption is NOT made by Linear Regression?Answer areaLinearity of relationshipsIndependence of errorsHomoscedasticityData follows a normal distribution

Step 1: Break Down the Problem

To identify which assumption is NOT made by Linear Regression, we need to analyze the four options provided:

1. Linearity of relationships
2. Independence of errors
3. Homoscedasticity
4. Data follows a normal distribution

Step 2: Relevant Concepts

Linear Regression relies on several key assumptions:

• Linearity: Assumes a linear relationship between the independent and dependent variables.
• Independence of Errors: Assumes that the residuals (errors) are independent from one another.
• Homoscedasticity: Assumes that the variance of errors is consistent across all levels of the independent variable.
• Normal Distribution of Errors: Linear Regression does not require the data itself to be normally distributed, but the errors must be normally distributed for inference purposes.

Step 3: Analysis and Detail

Now let's analyze each option:

1. Linearity of relationships: This is a fundamental assumption.
2. Independence of errors: This is also a required assumption.
3. Homoscedasticity: This condition is necessary for valid regression results.
4. Data follows a normal distribution: This is not a strict assumption for Linear Regression itself; rather, it pertains to the errors, not the data.

Step 4: Verify and Summarize

Upon examining each assumption, the fourth option regarding data following a normal distribution is the only one that does not apply as an assumption of Linear Regression.

Final Answer

The assumption that is NOT made by Linear Regression is: Data follows a normal distribution.