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 Management Information Systems

Week 2, Assignment 1

Correlation vs. Regression analyses (2 points)

Due date: Jan 29

Name:

ID:

I. Correlation Analysis

1.1 College basketball is big business, with coaches’ salaries, revenues and expenses in millions ofdollars. The data file Colleges- basketball contains the coaches’ salaries and revenues for college basketball at selected schools in a recent year.

a.  Compute the coefficient of correlation among the four attributes.

The coefficient of correlation between Salary and Expenses equals to 0.7732The coefficient of correlation between Salary and Revenues equals to 0.6092The coefficient of correlation between Salary and Winning% equals to 0.1159The coefficient of correlation between Expenses and Revenues equals to 0.768The coefficient of correlation between Expenses and Winning% equals to 0.0276

The coefficient of correlation between Revenues and Winning% equals to -0.1206

 b.  What conclusions can you reach about the relationship between, for example,

1) a coach’s salary and revenue – 

 by the result we got in a), which equals to 0.6092, I can state thatthe coach’s salary and revenue relationship is moderately positively correlated. 

2) salary and winning? - by the result we got in a), which equals to 0.1159 I can state that the salaryand revenue relationship is slightly positively correlated.

II. Regression analysis

2.1 The marketing manager of a large supermarket chain would like to use shelf space to predict the salesof pet food. A random sample of 12 equal sized stores is selected with the following result in the filePetfood.

a. Assuming a liner relationship, find the regression coefficients Bo and B1.The Simple Linear Regression Model Defines as Yi = β0 + β1Xi + εi, 

where regression coefficient Bo equals to 145regression coefficient B1 equals to 7.4

c.  Interpret the meaning of the slope, B1  B1 equals to 7.4, which means that by changing Xi by 1, the Yi will change by 7.4

d.  Find the p-value for shelf space and interpret the meaning of it.

The p-value for shelf space equals to 0.000906 and less than 0.1, which means that the probability of mistake is very low. So that in our case we can use the shelf space to predict the sales of pet food.

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e.  Predict the mean weekly sales of pet food for stores with 8 feet of shelf space for pet food.The Simple Linear Regression Model Defines as Yi = β0 + β1Xi + εi. Let’s put the variables: β0 = 145; β1 = 7.4; Xi = 8;Yi = 145 + 7.4*8=204.2 –  the prediction of mean weekly sales of pet food.

I. Correlation Analysis

1.2 The data file Wholefoods contains the price as calculated by owners and by current governmentstandards.

a. Compute the coefficient of correlation among four stores.The coefficient of correlation between Gristede's and Whole Foods equals to 0,8882The coefficient of correlation between Fairway and Whole Foods equals to 0,9715The coefficient of correlation between Stop&Shop and Whole Foods equals to 0,9817

The coefficient of correlation between Gristede's and Fairway equals to 0,9499The coefficient of correlation between Gristede's and Stop&Shop equals to 0,8828

The coefficient of correlation between Fairway and Stop&Shop equals to 0,9704

 b. What conclusions can you reach about the relationships among the four stores’ price levels? 

 By the results we have at the a), I can state that the prices relationships are strongly positively correlated.

II. Regression analysis

2.2 Circulation is the lifeblood of the publishing business. The larger the sales of a magazine, the more it

can charge advertisers. The data in the file Circulation represent the reported and audited newsstand sales.

a. Assuming liner relationship, find the regression coefficients Bo and B1.The Simple Linear Regression Model Defines as Yi = β0 + β1Xi + εi, 

where regression coefficient Bo equals to 26.72regression coefficient B1 equals to 0.57

 b. Interpret the meaning of the slope, B1. B1 equals to 0.57, which means that by changing Xi by 1, the Yi will change by 0.57

c. Find the p-value for reported sales and interpret the meaning of it.The p-value for shelf space equals to 0,0000268 and less than 0.1, which means that the probability ofmistake is very low.

d. Predict the mean audited newsstand sales for a magazine that reports newsstand sales of 400.

The Simple Linear Regression Model Defines as Yi = β0 + β1Xi + εi. Let’s put the variables:

 β0 = 26.72; β1 = 0.57; Xi = 400;

Yi = 26.72 + 0.57*400=254.72 –  the prediction of mean audited newsstand sales.