Correlation and Regression

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Discuss the relationship between independent and dependent variables with regard to correlation and regression analysis.

In both correlation analysis and regression analysis, you have two variables.

In correlation analysis, you are just interested in whether there is a relationship between the two variables, and it doesn't matter which variable you call the dependent and which variable you call the independent.
In regression analysis, you are examining the relationship between the two variables and trying to find a line that describes the data. In this case, it does matter which variable you call the independent variable and which variable you call the dependent variable. The independent variable is graphed on the x-axis, while the dependent variable is graphed on the y-axis. The independent variable is often the variable you can control or choose the values for.

See: http://www.graphpad.com/faq/viewfaq.cfm?faq=1141

Please explain which parts of the regression equation correspond to the independent and dependent variables. Then use the data set below to answer the questions from your boss below.

Newspaper Advertising ($000) Radio/TV Advertising ($000) SALES ($000)
40 0 973
40 0 1119
25 25 875
25 25 625
30 30 910
30 30 971
35 35 931
35 35 1177
25 40 882
25 40 982
45 45 1628
45 45 1577
0 50 1044
0 50 914
25 55 1329
25 55 1330
30 60 1405
30 60 1436
35 65 1521
35 65 1741
40 70 1866
40 70 1717

You need to have a question in mind before you choose independent and dependent variables. This is because the independent variable is the one you assume will affect the dependent variable.

Your boss wants to examine the relationship between print media and radio/TV and sales. In this scenario, we are assuming that advertising will predict or affect sales. Therefore, we have two independent variables: print advertising and radio/TV advertising. We have one dependent variable: sales.

You've been asked to develop a media spend model by your boss. She wants to know whether it makes more sense to invest in print media or radio/TV. She has a limited budget and wants the most bang for her buck. What do you suggest to her and why. She has a budget of exactly $38,000. She has asked you to predict what kind of return she can expect. Please use the output from your model to explain and support your recommendations.

Simple linear ...