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# Regression and Variable Case Studies

Please see the attached file for the two case studies.

MBA/510

1. A study is being undertaken of companies going public. Of particular interest is the relationship between the size of the offering and the price per share. A sample of ten companies that recently went public revealed:

Size Price
(millions) Per Share
Company X Y X2 XY
1 9.0 15.8 81.00 142.20
2 94.4 11.3 8,911.36 1,066.72
3 27.3 13.2 745.29 360.36
4 179.2 10.1 32,112.64 1,809.92
5 71.9 11.1 5,169.61 798.09
6 97.9 11.0 9,584.41 1,076.90
7 93.5 10.9 8,742.25 1,019.15
8 70.0 11.7 4,900.00 819.00
9 160.7 10.3 25,824.49 1,655.21
10 96.5 11.6 9,312.25 1,119.40

Total: 900.4 117.0 105,383.3 9,866.95

a. Determine the regression equation (show your work).

b. What does the slope of the regression equation tell us?

c. What would you predict the price per share to be if 95 million shares were offered?

2. Thompson Machine Works purchased several new, highly sophisticated machines. The production department needed some guidance with respect to qualifications needed by an operator. Four variables were listed.

X1 = Length of time employee was a machinist
X2 = Mechanical aptitude test score
X3 = Prior on -the-job rating
X4 = Age
Performance on the machine is designated Y

The following are the results of the regression analysis;

Independent
Variables Coefficient t-stat
Intercept 11.600 2.95
X1 0.400 1.23
X2 0.286 3.71
X3 0.112 4.10
X4 0.002 1.86

a. Write out the multiple regression equation.

b. How many independent variables are there?

c. Would you consider eliminating any of the independent variables?

3. Suppose the regression equation that has been used to estimate the value of existing homes is as follows;

Value = 10,000 + 50X1 + 5X2 + 10,000X3

Where;
X1 is square feet of livable area
X2 is the size of the lot measured in square feet
X3 is an indicator variable for the presence of a pool (1 if yes, 0 if no)

Interpret the meaning of the slopes of this equation.

#### Solution Preview

Please see the attached file for the solutions.

1. A study is being undertaken of companies going public. Of particular interest is the relationship between the size of the offering and the price per share. A sample of ten companies that recently went public revealed:

Size Price
(millions) Per Share
Company X Y X2 XY
1 9.0 15.8 81.00 142.20
2 94.4 11.3 8,911.36 1,066.72
3 27.3 13.2 745.29 360.36
4 179.2 10.1 32,112.64 1,809.92
5 71.9 11.1 5,169.61 798.09
6 97.9 11.0 9,584.41 1,076.90
7 93.5 10.9 8,742.25 1,019.15
8 70.0 11.7 4,900.00 819.00
9 160.7 10.3 25,824.49 1,655.21
10 96.5 11.6 9,312.25 1,119.40

Total: 900.4 117.0 105,383.3 9,866.95

a. Determine the regression equation (show your work).

We know that equation of the regression line

here given that from data ...

#### Solution Summary

This solution explains two case studies focusing on regression, slope and independent variables.

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