BUSA 2185: BUSINESS RESEARCH

BUSA 2185: BUSINESS RESEARCH

Short Exercise 4

Excel & SPSS Linear Regression Analysis and Analysis of Residuals

(25 points)

Your Name

Overview:
This assignment consists of three parts:

1. Simple Regression in Excel (8 points)
2. Simple Regression in IBM SPSS. (8 points)
3. Analysis of Residuals in IBM SPSS (7 points)
4. Simple Regression in Excel (Excel 2010, 2013, & 2016)
   · In the first part an example shown for this analysis using the GPAvsGMAT.xls data.
   · In the second part you have to repeat the same steps to for the IQvsGPA.xls
   · You have to provide the same screenshots and results as in the examples that I provided.
   1.1. EXAMPLE:
   · 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 Excel’s Data tab. 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:

a. Screenshot from Excel

b. Summary output for regression analysis from Excel

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

Note: If you are using Excel 2003 or 2007 version, you get the Data Analysis by following these steps:

• Simple Regression in Excel 2007
  To get the Data Analysis tool in Excel 2007, click on the Office button (top left corner), and select Excell options > Add-Ins > Go > Select Data Analysis Toolpack & Toolpack VBA. Data Analysis is now available under Excel’s Data tab.
• Simple Regression in Excel 2003
  To get the Data Analysis tool in Excel 2003, select Tools > Add-Ins > Select Data Analysis Toolpack & Toolpack VBA. Regression analysis is then available under Tools > Data Analysis

Regression.

1.2 Repeat these steps for the data of IQvsGPA.xls.

In the second part you have to repeat the same steps to for the IQvsGPA.xls
You have to provide the same screenshots and results as in the examples that I provided. Provide your output as shown in example. (8 points)
a. Screenshot from Excel (2 points)
b. Summary output for regression analysis from Excel (6 points)

1. Simple Regression in IBM SPSS
   EXAMPLE:

2.1 Start IBM SPSS Statistics 21, 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.

a. Screenshot from SPSS

2.1.1 Select Analyze > Regression > Linear. Specify Dependent=GPA, Independent=GMAT.

Select OK.

b. Summary output for regression analysis from SPSS

This will produce the following output:

Regression

Variables Entered/Removed b

Model

Variables Entered

Variables Removed

Method

1

GMAT a

.

Enter

a. All requested variables entered.

b. Dependent Variable: GPA

Model Summary

Model

R

R Square

Adjusted R Square

Std. Error of the Estimate

1

.809 a

.654

.635

.4350

a. Predictors: (Constant), GMAT

ANOVAb

Model

Sum of Squares

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), GMAT

b. Dependent Variable: GPA

Coefficientsa

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

B

Std. Error

Beta

1 (Constant) GMAT

-1.700

.008

.727

.001

.809

-2.338

5.831

.031

.000

a. Dependent Variable: GPA

2.2. Repeat these steps for the data of IQvsGPA.xls. Provide your output as shown above. (12.5 points)

In the second part you have to repeat the same steps to for the IQvsGPA.xls
You have to provide the same screenshots and results as in the examples that I provided.
a. Screenshot from SPSS (2 points)

b. Summary output for regression analysis from SPSS (6 points)

1. Analysis of Residuals in IBM SPSS (7 points)
   Refer to the IQvsGPA data. IBM SPSS to check on the three Regression Model assumptions Independence, Constant Variance, Normality.

Overview:
In the first part an example shown for this analysis using the GPAvsGMAT.xls data.
In the second part you have to repeat the same steps to for the IQvsGPA.xls and you have to provide the same tables and screenshots for IQvsGPA.xls.
3.1 Example:

Start IBM SPSS 22. Select File > Open > Data. Open GPAvsGMAT.xls (change file type to “Excel”).

Select Analyze > Regression > Linear and specify GPA as the Dependent and GMAT as the Independent variable.

To get SPSS to highlight any outliers, we click the Statistics button in the regression window, and check the box for Casewise Diagnostics. Note that the default value of standardized residual is 3, but you may want to replace it by 2 when you have a small sample size. Unusual observations, if any, will be displayed in a table in the output. Click Continue.

To study the Normality (or lack thereof) of the residuals, click the Plots button in the regression window, and select both the Normal Probability Plot and the related Histogram.

Remember that if Normality is present in the residuals, we would expect the points in the Probability Plot to fall on a straight line. From the Plots button menu we can also obtain a plot of the standardized residuals against (standardized) predicted values (of the dependent

2

variable). Select ZRESID and ZPRED from the menu (as y-axis and x-axis respectively). In this plot, we are hoping to see a random scatter. Look out for “funneling” patterns, illustrating that the variance is not constant, and functional relationship patterns, illustrating a deficiency in our model form.

3.2 Now, repeat these steps above to find out the three Regression Model Assumptions Independence, Constant Variance, Normality by using the IQvsGPA.xls data.

You have to provide the same tables and screenshots for IQvsGPA.xls.

Tip: You need to specify GPA as the Dependent and IQ as the Independent variable.

Paste the screenshots for each step as shown above.

9