Question

Construct a scatterplot, find the value of the linear correlation coefficient r, find the critical value of r from Table A-6 by using a 0.05, and determine whether there is a linear correlation between the two variables.

Song Audiences and Sales The table below lists the numbers of audience impressions (in hundreds of millions) listening to songs and the corresponding numbers of albums sold (in hundreds of thousands). The number of audience impressions is a count of the number of times people have heard the song. The table is based on data from USA Today. Does it appear that album sales are affected very strongly by the number of audience impressions?

Audience Impressions	/Album Sold
28	19
13	7
14	7
24	20
20	6
18	4
14	5
24	25
17	12

a. Linear correlation coefficient (r): Answer
b. Critical Value from Table A-6 (r): Answer
a. Is there linear correlation? Answer (Yes, there is linear correlation or There is not enough data)

Answer 1

Let's use excel:

Step 1) First enter the given data-set in excel columns

step 2) Select both the column and then click on Insert >>>Scatter >>>First image

Then we get the following output:

The linear correlation coefficient (r) is obtained by using "=CORREL(range of x, range of y)" this excel command.

and then enter

So we get r = 0.7959

a. Linear correlation coefficient (r): 0.7959

n = total number of pairs (x, y) = 9

degrees of freedom = n - 2 = 9 - 2 = 7

and level of significance = = 0.05

critical r using Pearson's correlation coefficient table is 0.666

b. Critical Value from Table A-6 (r): 0.666

Since critical r = 0.666 < 0.7959 = r so we reject null hypothesis.

Conclusion: There is sufficient evidence to support the claim of a linear correlation between the two variables.

a. Is there linear correlation Answer : Yes, there is linear correlation