True or False, In simple linear regression analysis, if the error terms exhibit a positive or negative autocorrelation over time, then the assumption of constant variance is violated.
True. In simple linear regression analysis, the assumption of constant variance, also known as homoscedasticity, is violated if the error terms exhibit a positive or negative autocorrelation over time.
To understand why this is true, let's break it down:
1. Autocorrelation: Autocorrelation refers to the correlation between the error terms of a regression model at different points in time. Positive autocorrelation indicates that a positive error at one point in time is likely to be followed by another positive error, and negative autocorrelation indicates that a positive error is likely to be followed by a negative error.
2. Constant Variance: The assumption of constant variance in a regression model, also called homoscedasticity, states that the variance of the error terms should be constant across all levels of the independent variable(s). In other words, the spread or dispersion of errors should be the same for all values of the independent variable(s).
Now, if the error terms exhibit a positive or negative autocorrelation over time, it means that the variance of the error terms is not constant. This violation of the assumption of constant variance can lead to biased and inefficient parameter estimates, incorrect standard errors, and unreliable hypothesis tests in the regression analysis.
In order to test for autocorrelation and determine if the assumption of constant variance is violated, statistical techniques such as Durbin-Watson test or graphical methods like plotting residuals over time can be used. If autocorrelation is present, further analysis such as autoregressive models or generalized least squares regression might be necessary to account for the violation of assumptions.