Regression Analysis in Finance: Understanding the Relationship between X and Y Variables, Lecture notes of Finance

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MSc Finance, MSc International Banking & Finance, MSc Investment & Finance, MSc International Accounting & Finance

Computing for Finance

and Financial Analysis

(Excel)

Lecture 7 - Semester 2

Regression Regression Basics Regression Equation Hypothesis Example

Regression Basics

Ordinary Least Squares Regression

Fits the best possible line to a set of data

Gives an indication of whether the X variable(s)

can explain the Y variable

The Regression Equation

Equation is of the form: Y=α+βX+

For example: R=α+βRm+

where: R is the return on a stock or asset Rm is the return on the market is the error term or residual α is the intercept (where the line crosses the y-axis)

The Regression Hypothesis R=α+βRm+ H 0 : β = Ha: β≠ 0 That is, test whether the X variable ( Rm ) has no effect on the Y variable ( R )

Testing the Hypothesis Two things required: a test statistic (provided by Excel regression) a critical value (depends on significance level, α/2) tcritical =NORMSINV(1-α/2)

Example 2 Can the FT All Share Index be explained by the movement of a subset of 6 of its component stocks? Rm=α+β 1 R 1 +β 2 R 2 +β 3 R 3 +β 4 R 4 +β 5 R 5 +β 6 R 6 +

Different ways to Regress Data Analysis : Regression Tool Functions: =SLOPE( y’s,x’s ) =INTERCEPT( y’s,x’s ) =LINEST( y’s,x’s ) array function Use Minitab instead!

Minitab or Excel?

Excel regression is:

Clear, simple, handy if your data is already in

Excel

Minitab regression is:

More powerful with series of regressions -

very easy to run lots of regression in a macro

& accumulate the results (STACK)