Linear Regression Question (Repost)

Question

To compare textbook prices at the two most popular online booksellers, a Statistics student gathered information about 14 college textbooks from Amazon.com and bn.com on November 25, 2006. For each book, she recorded the name of the principal author, the title, the ISBN, the Amazon selling price (in dollars) and the B&N selling price (in dollars):

author	title	ISBN	Amazon	B&N
De Veaux	Intro Stats	321286715	120.67	103.20
Christensen	Introduction to Statistics	155459651	164.95	155.95
Thomas	Calculus	321185587	154.67	152.00
Stewart	Calculus	534393217	153.98	155.75
Simmons	Calculus with Analytic Geometry	70576424	150.00	159.75
Alexander	American Public School Law	534274242	128.95	115.85
Miller	Business Law Today	324204841	108.95	103.95
Cheeseman	Business Law	131984934	166.67	159.60
Berg	Biochemistry	716787245	149.95	148.91
Raymond	General Organic and Biological Chemistry	471447072	95.95	98.95
Atkins	Chemical Principles	071675701X	141.95	139.75
Warren	Financial & Managerial Accounting	324188013	158.95	145.95
Kieso	Intermediate Accounting, Vol. 1	471771929	102.95	107.00
Garrison	Managerial Accounting	72834943	134.69	147.96

Compute the correlation between Amazon price and B&N price for these textbooks (Assume the correlation conditions have been satisfied and round your answer to the nearest 0.001.)

My apologies if the table is confusing, I am just confused about how to work the problem and what the answer is. Thank you!

Answer 1

Plotting the data shows a positive correlation.

To compute the correlation, you can use a calculator like a TI-84, typing the numbers into a list and pushing a button. But, I'm assuming you will need to do it manually.

The value of the correlation (called "r") is calculated using the equation:

r = [∑(x-xbar)(y-ybar)/√(∑(x-xbar)²•(∑(y-ybar)²) and is calculated using a table:

x               y            x – xbar     y – ybar         (x – xbar)(y – ybar)     (x – xbar)²    (y – ybar)²

120.67      103.20      -17.42         -32.13             559.69                              303.51            1032.11

164.95      155.95      26.86           20.62               553.92                              721.38            425.33

154.67      152.00      16.58           16.67               276.42                              274.85            278.01

153.98      155.75      15.89           20.42               324.50                              252.45            417.12

150.00      159.75      11.91           24.42               290.85                              141.81            596.51

128.95      115.85      -9.14            -19.48             178.04                              83.57               379.33

108.95      103.95      -29.14         -31.38             914.35                              849.22            984.48

166.67      159.60      28.58           24.27               693.70                              816.73            589.21

149.95      148.91      11.86           13.58               161.08                              140.63            184.51

95.95         98.95         -42.14         -36.38             1532.95                            1775.90          1323.24

141.95      139.75      3.86             4.42                 17.07                                 14.89               19.57

158.95      145.95      20.86           10.62               221.59                              435.08            112.86

102.95      107.00      -35.14         -28.33             995.43                              1234.92          802.39

134.69      147.96      -3.40            12.63               -42.97                               11.57               159.61

The mean of the x's in column 1 (x-bar) is 138.09

The mean of the y's in column 2 (y-bar) is 135.33

The sum of the 5th column (x – xbar)(y – ybar) is 6676.64

The sum of the 6th column (x – xbar)² is 7056.51

The sum of the tth column (y – ybar)² is 7304.28

So r = 6676.64/√(7056.51•7304.28) = 0.929982. Rounded to the nearest 0.001 that would mean r = 0.930