Question

2. It is a shiny morning, you are landing at Guarulhos Airport in Sao Paulo, Brazil. Sambapati, a very well-known Brazilian corporation has hired you as consultant for determining its cost of capital.   During the next following weeks, you are very busy in meetings, and doing financial modeling. One of your main concerns is that Sambapati is not a publicly traded company.

After some thinking you decide to go ahead and run a multiple regression analysis.   You have the following variables in your model:

                Sambapati Quarterly Earnings (SPTE)

                Sambapati Quarterly ROE (SPTROE)

                S&P Companies Quarterly Earnings (SPE)

                Bovepsa* Companies Quarterly Earnings (BOVE)

                               *Bovepsa is the Brazilian stock index

                Price to Book Ratio of the SP 500 Companies (PBSP)

You run the regression in STATA with 20 quarters of data.

At the end you produce the following model:

                               SPTE= 0.59 + 4.56 (SPE) – 3.45 (SPTROE) + 2.85 (BOVE) - 1.38(PBSP)

Required:

  

1. Interpret the meaning of each one of the coefficients of this model

  

Answer 1

In general, A Regression analysis gives us an equation to establish the statistical relationship between one or more predictor variables and the response variable. In multiple regression, the relationship is predicted by two or more variables. There are n independent variables and n+ 1 regression coefficients, including the constant.

Lets assume a multiple regression equation, Y = b0 + b1X1 +b2X2 ... bnXn

where Y is the dependent variable that we are trying to predict,

X1, X2 ...  are the independent variables you are using to predict it,

b1, b2 ...  are the coefficients or multipliers that describe the size of the effect the independent variables are having on r our dependent variable Y, and

b0 is the value Y is predicted to have when all the independent variables are equal to zero.

Each regression coefficient (b0, b1 ...) represents the change in Y relative to a one unit change in the respective independent variable (X1,X2 ...). i.e. b1 is the change in Y relative to a one unit change in X1, assuming all other independent variables constant.

SPTE= 0.59 + 4.56 (SPE) – 3.45 (SPTROE) + 2.85 (BOVE) - 1.38(PBSP)

- This equation tells us that Sambapati Quarterly Earnings (SPTE) is predicted to increase by 4.56 when the S&P Companies Quarterly Earnings (SPE) variable goes up by one,

decrease by 3.45 when Sambapati Quarterly ROE (SPTROE) goes up by one,

Increase by 2.85. when Bovepsa* Companies Quarterly Earnings (BOVE) increases by one

decrease by 1.38 when  Price to Book Ratio of the SP 500 Companies (PBSP) incrases by one

and is predicted to be 0.59 when all other variables i.e. SPE,SPTROE,BOVE and PBSP are zero..

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