Q1. Following is the data of 11 students who gave both BITS-SAT and JEE. Let $x_i$ denotes the
BIT-SAT score and $y_i$ denotes the JEE score of the $i^{th}$ individual out of 100.
X 40 42 56 58 62 67 73 75 77 80 84
Y 38 43 54 57 64 62 74 73 71 83 81
Answer the following questions,
a. Find the estimated regression line.
[10 points]
b. Find the $r^2$ value and interpret it. If you include a missing data point $x_{12} = 63$, $y_{12} = 67$,
how will your $r^2$ change (tell if it will increase or decrease and your reason)? [5 points]
c. Predict the JEE score of a student who obtained 70 percent in BITSAT.
[2 points]
e. Show that the least square estimator of the slope parameter is unbiased. [3 points]
