hw1_solutions_fall2012.pdf

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BUSI 6220 FALL 2012 HW1 SOLUTIONS

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1.1. Simple Regression in Excel (Excel 2010).

To get the Data Analysis tool, first click on File >Options > Add-Ins > Go > Select Data Analysis

Toolpack & Toolpack VBA. Data Analysis is now available under Excels Datatab. Open the

Excel Worksheet GPAvsGMAT.xls and select Data Analysis > Regression. Then fill out the

popup window as shown below, specifying GPA as the Y variable and GMAT as the X variable:

This will produce the output:SUMMARY OUTPUT

Regression Statistics

Multiple R 0.8086001

R Square 0.6538342

Adjusted R Square 0.6346027

Standard Error 0.4350142

Observations 20

ANOVA

df SS MS F Significance F

Regression 1 6.43372807 6.43373 33.9982 1.59668E-05

Residual 18 3.40627193 0.18924

Total 19 9.84

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%Lower 95.0% Upper 95.0%

Intercept -1.699561 0.72677682 -2.3385 0.0311 -3.22646284 -0.17266 -3.2264628 -0.17265997

GMAT 0.0083991 0.001440476 5.8308 1.6E-05 0.005372795 0.011425 0.0053728 0.01142545

1.1b. Simple Regression in Excel (Excel 2007).


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To get the Data Analysis tool in Excel 2007, first click on the Office button (top left corner), and

select Excell options > Add-Ins > Go > Select Data Analysis Toolpack & Toolpack VBA. DataAnalysis is now available under Excels Datatab.

1.1c. Simple Regression in Excel (Excel 2003).

Open the Excel Worksheet GPAvsGMAT.xls and select Tools > Data Analys is > Regression.Then fill out the popup window the same way as shown for Excel 2010. In case Data Analysis is

not found under Tools, add it under Tools > Add-Ins.

1.2. Simple Regression in IBM SPSS.

1.2.1.Start IBM SPSS Statistics 20, available from the Statistics menu of the standard COB PC

configuration. Select File > Open > Data. Select to see Files of type: Excel. Open

GPAvsGMAT.xls. Confirm that variable names should be read from the first row of data.

1.2.2. SelectAnalyze > Regress ion > Linear. Specify Dependent=GPA, Independent=GMAT.


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Select OK. This will produce the following output:

Regression

Variables Entered/Removed

b

ModelVariablesEntered

VariablesRemoved Method

1 GMATa . Enter

a. All requested variables entered.b. Dependent Variable: GPA

Model Summary

Model R R SquareAdjusted R

SquareStd. Error ofthe Estimate

1 .809a .654 .635 .4350

a. Predictors: (Constant), GMAT

ANOVAb

ModelSum ofSquares df Mean Square F Sig.

1 Regression 6.434 1 6.434 33.998 .000(a)

Residual 3.406 18 .189

Total 9.840 19

a. Predictors: (Constant), GMATb. Dependent Variable: GPA

Coefficientsa

Model

UnstandardizedCoefficients

StandardizedCoefficients

t Sig.B Std. Error Beta

1 (Constant) -1.700 .727 -2.338 .031

GMAT .008 .001 .809 5.831 .000

a. Dependent Variable: GPA


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1.3. Simple Regression in MINITAB.

1.3.1. Start MINITAB 16 for Windows, available from the Statistics menu of the standard COB

PC configuration. Select File > Open Worksheet. Select to see Files of type: Excel. Open

GPAvsGMAT.xls.

1.3.2. Select Stat > Regression > Regression.

Select OK. This will produce the output:

Regression Analysis: GPA versus GMAT

The r egress i on equat i on i sGPA = - 1. 70 + 0. 00840 GMAT

Predi ct or Coef SE Coef T PConst ant - 1. 6996 0. 7268 - 2. 34 0. 031GMAT 0. 008399 0. 001440 5. 83 0. 000

S = 0. 435014 R- Sq = 65. 4% R- Sq( adj ) = 63. 5%Anal ysi s of Vari ance

Source DF SS MS F PRegr essi on 1 6. 4337 6. 4337 34. 00 0. 000Resi dual Err or 18 3. 4063 0. 1892Tot al 19 9. 8400


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1.4. Simple Regression in SAS 9.3Open SAS 9.3. IN the SAS environment, you will need to create a library called BUSI6220 and

convert the data file GPAvsGMAT.xls from Excel format to SAS format.

1.4.1. Double-click the yellow libraries icon. Right-click > New. Type BUSI6220 as the name ofthe new library, and an appropriate folder location in the Path box. Click OK. Your new library

should now appear as a new yellow icon.

1.4.2. Import the Excel data file by selecting File > Import Data > MS Excel > Next. Find your

file and select it. Select BUSI6220 as the destination library and GPAVSGMAT as the Member

name.1.4.3. Select Solutions > Analysis >Interactive Data Analysis. Select SAS data file

BUSI6220.GPAVSGMAT. Click Open.

1.4.4. Select Analyze > Fit. Specify GPA as the Y variable and GMAT as the X variable. Click

OK.


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The analysis results will appear as shown below.

GPA = GMAT

Response Di st r i but i on: Normal

Li nk Funct i on: Ident i ty

Model Equat i onGPA = - 1.6996 + 0.0084 GMAT

400 500 600

GMAT

1. 5

2. 0

2. 5

3. 0

3. 5

G

P

A

Summary of Fi t

Mean of Response 2.5000Root MSE 0. 4350

R-Square 0. 6538Adj R-Sq 0. 6346

Anal ysi s of Var i ance

Source

ModelErrorC Tot al

DF

1 18 19

Sumof Squares

6.4337 3.4063 9.8400

Mean Square

6.4337 0.1892

F St at

34.00

Pr > F

F F


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1.5b. Find the LSE solution for b0, b1, using Excel Solver (Excel 2010).

1.5.1. Start by setting up an Excel worksheet where the squared residuals are calculated. Use

arbitrary values for b0and b1(the arbitrary solution b0=-1.00 and b1=0.10 is shown below).

1.5.2. Fill in the rest of the worksheet, and place the sum of squared residuals in one of the cells:

To add solver in your Excel, follow similar steps as those involved in adding Data Analysis

capabilities. Solver will then be available under Excels Datatab.

1.5b.3. Set up a linear program using Solver (Data > Solver). Click Solveand keep the solution.The results will appear in cells B23 (for b0) and B24 (for b1). Solver will replace the arbitrary

values for b0 and b1 with the LSE solution values.

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hw1_solutions_fall2012.pdf