Homework 8

Note this homework is worth 20 points, 5 of them bonus.
Use MINITAB to confirm your answers. Because you then know if your answers are wrong there will be no partial credit for this homework. Do not hand in any MINITAB results.

Problem 1: Consider the following dataset:

x 0 1 2 3 4 5 6 7 8

y 0.5 1.2 1.4 3.9 5.3 6.1 6.0 7.1 7.9

Find Pearson's correlation coefficient r for this data. Do the work by hand and show all steps. Here is what is required:
n=
∑x=
∑y=
∑x²=
∑y²=
∑xy=

x	0	1	2	3	4	5	6	7	8
y	0.5	1.2	1.4	3.9	5.3	6.1	6.0	7.1	7.9

S_xx=
S_yy=
S_xy=

r = S_xy/√(S_xxS_yy) =

Problem 2
Say z=12.3x-4.8, then

z -4.8 7.5 19.8 32.1 44.4 56.7 69.0 81.3 93.6

y 0.5 1.2 1.4 3.9 5.3 6.1 6.0 7.1 7.9

Compute the correlation coefficient of z and y by hand to confirm that it is the same as the correlation coefficient of x and y. Again write down all the intermediate steps.

Problem 3 For the data in problem 1 find the least squares regression line y=b₀+b₁x

Problem 4 For the data in problem 1 find the least squares regression line x=b₀+b₁y

Problem 5 Draw the scatterplot of y vs x (with x on the x-axis). Add the least squares regression lines of y vs. x and x vs. y (Careful: the graph always has x on the x-axis!)

z	-4.8	7.5	19.8	32.1	44.4	56.7	69.0	81.3	93.6
y	0.5	1.2	1.4	3.9	5.3	6.1	6.0	7.1	7.9