STAT XL 10

Introduction to Statistical Reasoning

Instructor: Ivo Dinov, Asst. Prof.

Departments of Statistics & Neurology
 http://www.stat.ucla.edu/~dinov/

Due Date:

Wednesday, May 22, 2002, turn in before lecture

See the HW submission rules . On the front page include the following header .

• (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/