Are these questions below true or false? I am stuck. I think 1 is true and 3 is false
1. In Regression Analysis if the variance of the error term is constant, we call it the Homoscedasticity property.
2. 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.
3. The expected value of the error term changes from observation to observation.
To determine if the statements are true or false, let's break down each statement and evaluate them individually:
1. In Regression Analysis, if the variance of the error term is constant, we call it the Homoscedasticity property.
This statement is TRUE. In regression analysis, when the variance of the error term is constant across all levels of the independent variable(s), it is referred to as the Homoscedasticity property. Homoscedasticity assumes that the variability of the errors is consistent across the entire range of values of the predictor variable(s).
To confirm this, you can refer to statistical textbooks, online resources, or regression analysis literature that discuss the Homoscedasticity assumption in regression analysis.
2. 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.
This statement is TRUE. Autocorrelation refers to the correlation between the error terms in a regression model across different observations. If there is a pattern or correlation between the error terms over time, it violates the assumption of independence and can lead to biased parameter estimates.
However, this statement does not directly relate to the assumption of constant variance (homoscedasticity). Autocorrelation affects the efficiency and validity of the regression estimates but is not directly linked to constant variance violation.
3. The expected value of the error term changes from observation to observation.
This statement is FALSE. The expected value of the error term is assumed to be constant and equal to zero in regression analysis. This assumption is necessary for unbiased parameter estimates. If the expected value of the error term changes from observation to observation, it implies that the errors are not centered around zero, which violates the assumption.
To determine the expected value of the error term, you can refer to the assumptions of linear regression in statistical textbooks or regression analysis literature.
To summarize, the correct evaluations for the statements are as follows:
1. True
2. True
3. False