In Chapter 4, we discussed seven explicit assumptions about the properties of a regression equation. These assumptions (or, more accurately, the first six of them) are usually referred to as the Classical Assumptions.
(a) Carefully and accurately state the seven assumptions.
(b) State what each assumption actually means in real-world terms (be extremely brief).

Question

Quizplus · Accepted Answer

The Answer is (a) The seven assumptions about the properties of a regression equation are:

1. Linearity: The relationship between the independent and dependent variables is linear.
2. Independence: The errors in the regression model are independent of each other.
3. Homoscedasticity: The variance of the errors is constant across all levels of the independent variables.
4. Normality: The errors in the regression model are normally distributed.
5. No perfect multicollinearity: There is no perfect linear relationship between the independent variables.
6. Zero conditional mean: The expected value of the error term is zero given the values of the independent variables.
7. No autocorrelation: The errors in the regression model are not correlated with each other.

(b) The real-world meanings of these assumptions are:

1. Linearity: The relationship between the independent and dependent variables can be represented by a straight line.
2. Independence: The errors in the regression model are not influenced by each other.
3. Homoscedasticity: The variability of the errors is consistent across different levels of the independent variables.
4. Normality: The errors in the regression model follow a normal distribution.
5. No perfect multicollinearity: There are no exact linear relationships between the independent variables.
6. Zero conditional mean: The average value of the errors is zero given the values of the independent variables.
7. No autocorrelation: The errors in the regression model do not exhibit a pattern of correlation over time.

In Chapter 4, We Discussed Seven Explicit Assumptions About the Properties