How to Do a Regression in Excel 2007

7/29/2019 How to Do a Regression in Excel 2007

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David Acquaye BSc. MBA, PhD-St. (2010/11)

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How to do a regression in Excel 2007+

The following procedure can be followed to do a regression in Excel using office

2007 or 2010.

Step 1 : Input your data.

Step 2 : Click on Data - Click on the Data Analysis Tab

Just enter

your data.


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i. Click on the Office button and Select Excel Options

ii. Click on the Excel options and Select Add-ins


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iii. Select Analysis Tool Pak or The first Add-in which appear on your version.

You may have Analysis ToolPak or Analysis ToolPak-VBA from the Add-In Window

iv. Click on Go and Select activate Analysis ToolPak


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Step 3 : Start your regression by clicking on the Data Analysis Tab and SelectRegression from the Menu which appears.

Step 4 : Input your Dependent Variable in (Y) and your Independent Variable in X. For this exampleour dependent Variable is Sales and our Independent Variable is Advertising.


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Click on Labels, Confidence Level and Line Fit Plots etc :

Step 5 : Click on Ok Interpret your results and Add Trend Line by Clicking on the

Scatter plots.


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SUMMARY OUTPUT

Regression Statistics

Multiple R 0.640163

R Square 0.409808

Adjusted R Square 0.26226

Standard Error 0.666976

Observations 6

ANOVA

df SS MS F Significance F

Regression 1 1.235571 1.235571 2.777456647 0.170928

Residual 4 1.779429 0.444857

Total 5 3.015

CoefficientsStandard

Error t Stat P-value Lower 95%Upper95%

Intercept 6.890714 1.265289 5.445961 0.005521213 3.377709 10.40372

Advert Exp ('000) 0.006643 0.003986 1.66657 0.170928062 -0.00442 0.01771

The Regression has three components:

1. Regression Statistics Table2. ANOVA Table3. Regression Coefficient Table

Regression Statistics Table:

SUMMARYOUTPUT

Regression Statistics

Multiple R 0.64016256

R Square 0.4098081

Adjusted R Square 0.26226013

Standard Error 0.66697612

Observations 6

Explanation :

The above gives the goodness-of-fit measures :R2 = 40.98%


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The correlation between the dependent variable (Sales) and Independent Variable (AdvertisingExpenditure is 0.64-Multiple R. When this is squared we get R2. There 0< R2 < 1. The more closer weare to 1 the more the variation is explained.

Therefore R Square = 0.409 or 40.98% means that 40.98% of the variations in sales is explained by theAdvertising. When there is more than more than one independent variable it is better to use theAdjusted R square.

The standard error of the regression is 0.66697

Analysis of the Variance : ANOVA

ANOVA

df SS MS F Significance F

Regression 1 1.235571 1.235571 2.777456647 0.170928

Residual 4 1.779429 0.444857

Total 5 3.015

This splits the sum of squares into its components:SS, MS will be discussed later

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This splits the sum of squares into its components:SS, MS will be discussed later

Statistical Significance of the regression as whole.Here we use the F statistic. From the above the F statistic is 2.777 with a probabilityof 0.1709. It is normally the same as the p-value when only one independent variableis used. This means the entire regression is not statistically significant at the 95%confidence level (5% level of significance)

3. Regression Coefficient Table

CoefficientsStandard

Error t Stat P-valueLower95%

Upper95%

Intercept 6.890714286 1.265288948 5.445961016 0.0055212 3.377709 10.40372Advert Exp('000) 0.006642857 0.003985945 1.666570325 0.1709281

-0.0044239 0.0177096

a. Regression Equation :Sales = 6.890 + 0.0066Advert [Using the Coefficient Column]

This should be explained under the following headings :

Size and Sign :


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Sign :From the very beginning we expect Sales to be related to advertising. It is seenfrom the equation that sales is positively related to advertising (If we needmore sales we need to do advert). This can also be supported with theMultiple R which is the same as the correlation.

Size :If there is no advert (i.e Advert = 0) then Sales will be 6.890 (m). Sales willrise by 0.0066 (000,000) or 6600 for a unit increase in advertising (ie 1000).

b. Statistical Significance of Coefficients :This can be done using the p-values or the critical t values. If we performregression at the 95% level or at the 5% percent level of significance then thefollowing applies :

If p < 0.05 : Statistically significant ; p > 0.05 : Statistically not significant.

From the regression above the p>0.05 which means that the relationship foundbetween advertising and sales is not statistically significant.

Example 2 Multiple Regression

A car dealer believes the number of cars sold each month is related to the number of

years of sales experience and the age of the sales person. The data for a randomsample of 10 sales persons are as follows:

Y X1 X2

17 2 23

23 6 33

20 8 30

18 11 35

19 4 24

22 7 49

21 7 36

28 14 40

26 12 46

12 3 51

Y = number of cars sold per month, X1 = Number of years of sales experience and X2=Ageof Sales person (Years).

Required :Using a multiple regression analysis and use your output to perform the following :


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i. What is the estimated regression Equation?

ii. Interpret the coefficient s on X1 and X2.

iii. State whether or not there is a significant relationship between sales and bothexplanatory variables, taken together, at the 5% level of significance.

iv. State whether or not the explanatory variables X1 and X2 are statisticallysignificant at the 5% level . Be sure to state the null and alternative hypothesisand on what your conclusions are based (i.e. the test procedure used).

Example 3

MonthsSales(000) Price ()

Advert Exp() Mean Daily Hours

January 75 6.8 2 2.4

February 90 6.5 5 4

March 148 6 6 5.2

April 183 3.5 7 6.8

May 242 3 22 8

June 263 2.9 25 8.4July 278 2.6 28 10.4

August 318 2.1 30 11.5

September 256 3.1 22 9.6

October 200 3.6 18 6.1

November 140 4.2 10 3.4

December 80 5.2 2 2

Perform a regression analysis and Discuss under the following headings:

a. Explanatory power of the regressionb. The regression Equationc. The Statistical Significance of the Independent Variable


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When the trend line is added, this is what we get:

Reference:

Fleming M.C and Nellis, J.G (1997) Statistics for Business, Prentice Hall, UK

Curwin, J and Slater, R (2004), Quantitative Methods for Business Decisions, 5th Edition,

Thomson, UK

y = 0.0066x + 6.8907

0

2

4

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0 100 200 300 400 500

Sa

les('m)

Advert ('000)

Regression Model for Sales on Advertising

Sales

Predicted Sales

Linear (Predicted Sales)

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How to Do a Regression in Excel 2007

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