PDF Notes: Lecture18_260424_093657

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    What should be checked after estimating a linear model?

    Data must meet model assumptions.

    What are residuals in a linear model?

    Estimates of the errors in predictions.

    How do residuals differ from errors?

    Residuals are not independent; they are based on predictions.

    What is the implication of E(ê;) = 0?

    The average of the residuals is zero.

    What does var(ê;) depend on?

    It depends on the distance of observations from the mean.

    What are studentized residuals?

    Standardized residuals used for diagnostics.

    What distribution do studentized residuals approximate?

    They approximate a standard normal distribution.

    What is the first assumption of the linear model?

    The relationship between E(Y;) and x; is linear.

    How can the first two assumptions be checked?

    By plotting studentized residuals against x;.

    What indicates the third assumption is met?

    Empirical quantiles of residuals align with normal quantiles.

    What happens if the quadratic term is included in the model?

    It improves the fit of the model.

    What is the purpose of multiple linear regression?

    To include multiple explanatory variables in the model.

    What is the criterion for estimating coefficients in regression?

    Minimizing the sum of squared residuals.

    What does the matrix notation of regression represent?

    It simplifies the representation of multiple variables.

    What is the significance of the F-statistic in regression?

    It tests if at least one coefficient is non-zero.

    What does the adjusted R-squared account for?

    It adjusts for the number of parameters in the model.

    How is the residual analysis conducted?

    By comparing studentized residuals to theoretical quantiles.

    What is the formula for the variance of residuals?

    It relates to the distance of observations from the mean.