Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematical Science Statistics & Exploratory Data Analysis Simple and Multiple Linear Regression
Consider the simple linear regression model Yi = βxi + ϵi, for i = 1, …, n; where E(ϵi) = 0, Cov(ϵi, ϵk) = 0 if i ≠ k and Var(ϵi) = \(\rm x_i^2 \sigma^2\). The best linear unbiased estimator of β is:
1
\(\rm\frac{\displaystyle\sum_{i=1}^n Y_i x_i}{\displaystyle\sum_{i=1}^n x_i^2}\)
2
\(\rm\frac{\displaystyle\sum_{i=1}^n Y_i}{\displaystyle\sum_{i=1}^n x_i}\)
3
\(\rm\frac{1}{n}\displaystyle\sum_{i=1}^n \frac{Y_i}{x_i}\)
4
\(\rm\frac{1}{n}\displaystyle\sum_{i=1}^n \frac{Y_i x_i}{x_i^2}\)