(HW_3_1) Compute the correlation coefficient, R(X,Y), for the following data. Interpret your result. Please do this by hand and show all of your
work. Find a linear equation, a line lo, which describes the best linear regression fit
(least squares fit) of Y on X. If we have two other candidate lines, l1 and l2, each with residual square error (RSE ) of 123 and 153, respectively. Compute the RSE for the best (least squares) line you computed, lo, and rank the three lines best to worst fit. What is your ranking criterion?
X
Y
1
0
3
1
5
4
7
7
9
8
What is the correlation R(Y, X)? R(3X-2.2 , -4Y +7)?
(HW_3_2) Find the equation of the line, l1,
passing through the points (-3, 5) and (1, 2). Identify the slope,
m1, and Y-intercept, b1, of the
line. A line, l2, is perpendicular to l1 if
its slope is -1/m1. Find the equation
of the line, l2, perpendicular to l1, which
goes through the point (X=0, Y=3). What are l2's slope,
m2, and Y-intercept, b2?
\Ivo D. Dinov, Ph.D., Departments of Statistics and Neurology, UCLA School
of Medicine/