## STAT 10

(Sec. 5a-5c)

Introduction to Statistical Reasoning

## Instructor: Ivo Dinov, Asst. Prof.

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

Due Date:

# Friday, Wed. 20, 2002, turn in after lecture

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

• (HW_4_1) Can an estimator be unbiased, but imprecise? For the following data what is an unbiased estimator of the population mean? Compute the corresponding estimate [the sample average] and its precision [ StdError(sample avg.)].

•  2 5 9 2 3 7 11 2 3 6 4 4 7 6 6 10 4 3 5 7

• (HW_4_2) Compute the correlation coefficient, R(X,Y) ,  for the following data. Please do this by hand and show all of your work. Find a linear equation which describes the best linear regression fit (least squares fit) of Y on X.
•  X Y 1 0 3 1 5 4 7 7 9 8

• (HW_4_3) 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/