# The Assumptions underlying regression

Regression analysis is a statistical technique used to model the relationship between a dependent variable and one or more independent variables. It is important to consider the assumptions underlying regression analysis to ensure the validity and reliability of the results. Here are some key assumptions:

Linearity: The relationship between the dependent variable and independent variables is assumed to be linear. This means that the change in the dependent variable is proportional to the change in the independent variables.

The Assumptions underlying regression in psychology-Non-linear relationships may require different modeling techniques.

Independence: The observations in the dataset are assumed to be independent of each other. This means that the value of one observation does not affect the value of another observation.

The Assumptions underlying regression in psychology-Independence can be violated when there is clustering or autocorrelation in the data.

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Homoscedasticity: Homoscedasticity assumes that the variability of the errors (residuals) is constant across all levels of the independent variables. In other words, the spread of the residuals should be consistent across the range of predicted values.

The Assumptions underlying regression in psychology-Heteroscedasticity occurs when the variability of the residuals differs across the levels of the independent variables.

Normality: The residuals in regression analysis are assumed to be normally distributed. This assumption is necessary for conducting hypothesis tests, constructing confidence intervals, and making valid statistical inferences. Departures from normality can affect the accuracy and reliability of the regression estimates.

No Multicollinearity: Multicollinearity refers to a high degree of correlation between independent variables in the regression model. It can cause problems in interpreting the individual effects of the independent variables and lead to unstable coefficient estimates. Multicollinearity can be assessed using correlation matrices or variance inflation factors (VIF).

No Endogeneity: Endogeneity occurs when there is a correlation between the independent variables and the error term in the regression model. This violates the assumption of independence and can lead to biased coefficient estimates.

The Assumptions underlying regression in psychology-Endogeneity can arise from omitted variables, measurement errors, or simultaneity.

No Outliers or Influential Observations: Outliers are extreme values that have a disproportionate impact on the regression results. Influential observations are data points that strongly influence the regression estimates. It is important to identify and assess the impact of outliers and influential observations on the regression model.

Stationarity: In time series regression, the assumption of stationarity is important. Stationarity implies that the statistical properties of the data, such as mean and variance, remain constant over time. Violations of stationarity can affect the accuracy of the regression results.

These assumptions provide the foundation for valid regression analysis. Violations of these assumptions can lead to biased estimates, incorrect inferences, and unreliable predictions.

The Assumptions underlying regression in psychology-It is essential to assess and address these assumptions to ensure the validity and interpretability of the regression model.