Properties of least squares estimates
Least squares estimates are a type of statistical estimation technique used to estimate the parameters of a linear regression model. The properties of least squares estimates include:
1. Unbiasedness: Least squares estimates are unbiased, meaning that the expected value of the estimates is equal to the true value of the parameters.
2. Consistency: Least squares estimates are consistent, meaning that as the sample size increases, the estimates become more accurate.
3. Efficiency: Least squares estimates are efficient, meaning that they have the smallest variance among all unbiased estimators.
4. Normality: Least squares estimates are normally distributed, meaning that the distribution of the estimates follows a normal distribution.
5. Invariance: Least squares estimates are invariant, meaning that they are not affected by changes in the scale of the data.