Discuss the assumptions underlying linear regression, and elaborate on their relevance for accurately interpreting model output.

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Anonymous · Accepted Answer

Linear regression is a widely used statistical method for modeling the
relationship between a dependent variable and one or more independent variables.
However, for linear regression to produce valid results, certain assumptions
must be met. Understanding these assumptions is crucial for accurately
interpreting the model output.

KEY ASSUMPTIONS OF LINEAR REGRESSION:

1. Linearity:Assumption: The relationship between the independent variables and
    the dependent variable is linear.
    Relevance: If this assumption is violated (e.g., the relationship is
    quadratic or logarithmic), the model may provide biased estimates and poor
    predictions. Non-linear relationships can lead to systematic errors.
    
 2. Independence:Assumption: The residuals (errors) are independent of each
    other.
    Relevance: If the residuals are correlated (e.g., in time series data), it
    can lead to underestimated standard errors and misleading significance
    tests. This violates the assumption of independence and can produce
    unreliable predictions.
    
 3. Homoscedasticity:Assumption: The variance of the residuals is constant
    across all levels of the independent variables.
    Relevance: If heteroscedasticity (non-constant variance) is present, it can
    lead to inefficient estimates and affect the reliability of hypothesis
    tests. It can indicate that the model may not adequately capture the
    relationship or that there are omitted variables.
    
 4. Normality of Residuals:Assumption: The residuals are normally distributed.
    Relevance: While normality is not strictly necessary for estimating the
    coefficients, it is important for conducting hypothesis tests (like t-tests
    for coefficients). Non-normal residuals can lead to incorrect conclusions
    about the significance of the predictors.
    
 5. No Multicollinearity:Assumption: Independent variables are not too highly
    correlated with each other.
    Relevance: Multicollinearity can inflate the standard errors of the
    coefficients, making it difficult to determine the individual effect of each
    predictor. This can lead to unreliable estimates and difficulty in
    interpreting the model.
    
 6. No Autocorrelation:Assumption: The residuals are not correlated with each
    other, especially in time series data.
    Relevance: Autocorrelation can indicate that important variables or time
    effects are missing from the model, leading to biased estimates and
    inefficient predictions.

Discuss the assumptions underlying linear regression, and elaborate on their relevance for accurately interpreting model output.

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