(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?