Teaching CSIR NET Mock Test Series Mathematical Science Statistics & Exploratory Data Analysis Simple and Multiple Linear Regression
Consider a linear regression model Y = α + βx + ε, where α and β are unknown parameters, and ε is a random error with mean 0. Based on 10 independent observations (xi, yi), i = 1, ..., 10, the fitted model, using OLS is
\(\rm\hat{y}_i=1.5+0.8 x_i,\) i = 1, 2, ..., 10.
Suppose that \(\sum_{i=1}^{10}\left(y_i-\frac{1}{10} \sum_{j=1}^{10} y_j\right)^2=5\) and \(\sum_{i=1}^{10}\left(x_i-\frac{1}{10} \sum_{j=1}^{10} x_j\right)^2=6\).
Then the adjusted coefficient of determination (adjusted R2) is equal to (after rounding off to two places of decimal)
1
0.74
2
0.83
3
0.77
4
0.84