Question

	X	Y
Obs 1	-3	2
Obs 2	-2	1
Obs 3	1	2
Obs 4	2	0
Obs 5	2	-5

Consider a random sample of 5 paired measurements in the following format. It is easy to demonstrate that the sample mean of each variable is 0.

Using Microsoft Excel, compute the following:

1. Calculate the sample standard deviation of X.
2. Calculate the sample standard deviation of Y.
3. Calculate the covariance of X and Y.
4. Calculate the correlation coefficient of X and Y.
5. Are your answers to any of the previous letters the same as in the previous example?
   1. Calculate the ratios of your answers in 2a, 2b and 2c to your answers in 1a, 1b and 1c respectively.
   2. If n=5, what is n-1?
6. Using Microsoft Excel, run a regression output from the Data Analysis ToolPak.
7. If you don’t know how to do this, Zoom me.
8. Does the sum of squares regression look like the squared norm of a vector from Question 1? If so, state what it is.
9. Does the sum of the squares residual look like the squared norm of a vector from Question 1? If so, state what it is.
10. Does the slope of the least squares regression line appear anywhere in your calculations in question ? If so, what is it?

Answer 1