Correlation analysis
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In these two exercises, construct a scatter plot, find the value of the linear correlation coefficient r, find the critical value of r from Table A-6 by using α = 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 28 13 14 24 20 18 14 24 17
Albums sold 19 7 7 20 6 4 5 25 12
State Budget and Days Late New York State has become notorious for approving the state budget after the annual deadline of April 1. The amount of the budget (in billions of dollars adjusted for inflation) and the number of days late are listed below with corresponding entries representing the same year. (The data are in order by row.) Does it appear that the size of the budget affects the number of days that the budget is late? Use a 0.05 significance level.
Budget
101 96 91 85 80 73 71 66 63 63
62 58 55 52 49 46 44 40 37 35
Number of Days Late
133 44 45 124 34 125 13 125 103 67
68 4 1 64 48 18 19 10 4 4
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Solution Summary
The solution provides step by step method for the calculation of correlation analysis. Formula for the calculation and Interpretations of the results are also included.
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