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# Correlation and Regression

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

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'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.

* What is the purpose of using correlation analysis? How may correlation analysis be used in business decisions or in relation to strategy formulation and implementation? How do correlations relate to the concept of partitioning of the variance in a regression model? How would correlation usage relate to any of the decisions you made in the first question? Did correlations support your decision? Did they support whatever model you recommended?

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#### Solution Preview

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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.

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.

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 ...

\$2.19

## Linear Correlation, Regression Lines and Measures of Variation

1) Testing for a Linear Correlation
Construct a scatter plot, find the value of the linear correlation coefficient r, and find the critical values of r from the table below using a=0.05. Determine whether the is sufficient evidence to support a claim of a linear correlation between the two variables.

Airline Fares Listed below are the costs (in dollars) of flights from New York (JFK) to San Francisco for US Air, Continental, Delta, United, American, Alaska, and Northwest. Use a 0.05 significance level to test the claim that there is no difference in cost between flights scheduled one day in advance and those scheduled 30 days in advance. What appears to be a wise scheduling strategy?

Flight scheduled 30 days advance 244 260 264 264 278 318 280
Fight scheduled one day in advance 456 614 567 943 628 1088 536
Create scatter plot

2) Finding the Equation of the Regression Line and Making Predictions
In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in
CPI and Subway Fare ; Find the best predicted cost of a slice of pizza when the consumer price index is 182.5 in the year 2000

CPI 30.2 48.3 112.3 162.2 191.9 197.8
Pizza 0.15 0.35 1.00 1.35 1.50 2.00

3) Finding the Equation of the Regression Line and Making Predictions
In each case, find the regression equation, letting the first variable be the predictor (x) variable. Find the indicated predicted value by following the prediction procedure summarized in

Commuters and Parking Space The Metro-North Station of Greenwich, CT has 2804 commuters . Find the best predicted number of parking spots at that station. Is the predicted value close to the actual value of 127?

Commuters 3453 1350 1126 3120 2641 277 579 2532
Parking Spots 1653 676 294 950 1216 179 466 1454

4) Finding Measures of Variation
Find (a) explained variation, (b) unexplained variation,(c) total variation, (d) coefficient of determination,and (e) standard error of estimate Se, In each case, there is sufficient evidence to support a claim of a linear correlation so that it is reasonable to use the regression equation when making predictions

CPI and Subway Fare The consumer price index and the cost of a slice of pizza from table 10-1
CPI 30.2 48.3 112.3 162.2 191.9 197.8
Pizza 0.15 0.35 1.00 1.25 1.75 2.00

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