Expected mean
Definition
The expected mean in the context of linear regression is the average value of the response variable predicted by the regression equation for a given set of predictor variables. It represents the central tendency around which individual observations are expected to vary.
5 Must Know Facts For Your Next Test
- The expected mean is calculated using the regression equation: $$\hat{Y} = b_0 + b_1X$$, where $$b_0$$ is the intercept and $$b_1$$ is the slope.
- It provides an estimate of the dependent variable based on values of one or more independent variables.
- The accuracy of the expected mean depends on how well the model fits the data, which can be assessed using R-squared and residual plots.
- In multiple linear regression, the expected mean extends to include multiple predictors: $$\hat{Y} = b_0 + b_1X_1 + b_2X_2 + ... + b_nX_n$$.
- It is important to check for assumptions like linearity, independence, homoscedasticity, and normality when interpreting the expected mean.
Review Questions
- What formula is used to calculate the expected mean in simple linear regression?
- Why is it important to check for assumptions like linearity and homoscedasticity when interpreting the expected mean?
- How does multiple linear regression extend the concept of expected mean?
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Related terms
Regression Equation: A mathematical formula that describes the relationship between one or more predictor variables and a response variable.
R-Squared: A statistical measure that indicates how much of the variance in the dependent variable is explained by the independent variable(s) in a regression model.
Residuals: The differences between observed values and their corresponding predicted values from a regression model; they indicate how well or poorly a model fits each observation.
