(1) Estimate a multiple regression equation with the price-earnings ratio (P/E)
ID: 3375755 • Letter: #
Question
(1) Estimate a multiple regression equation with the price-earnings ratio (P/E) as the dependent variable and the following as independent variables: intercept, gross profit margin, sales growth, dummy variable for industry 1, and dummy variable for industry 2.
(2 ) Create a set of dummy variables for each of the three industries.
(3) Interpret the regression results:
(a) adjusted R-square
(b) F-statistic
(c) t-statistics for each of the coefficients
(4) Calculate a P/E ratio point estimate for a firm with the following characteristics:
(a) gross profit margin = 16%
(b) sales growth = 13%
(c) operates in the oil industry
Firm P/E Ratio Gross Profit Margin (%) Sales Growth (%) Industry Abbott Laboratories 22.3 23.7 10.0 2 American Home Products 22.6 21.1 5.3 2 Amoco 16.7 11.0 16.5 1 Bristol Meyers Squibb Co. 25.9 26.6 9.4 2 Chevron 18.3 11.6 18.4 1 Exxon 18.7 9.8 8.3 1 General Electric Company 13.1 13.4 13.1 3 Hewlett-Packard 23.3 9.7 21.9 3 IBM 17.3 11.5 5.6 3 Merck & Co. Inc. 26.2 25.6 18.9 2 Mobil 18.7 8.2 8.1 1 Pfizer 34.6 25.1 12.8 2 Pharmacia & Upjohn, Inc. 22.3 15.0 2.7 2 Procter & Gamble Co. 5.4 14.9 5.4 3 Texaco 12.3 7.3 23.7 1 Travelers Group Inc. 28.7 17.8 28.7 3Explanation / Answer
Here I change lable of variables for my
simplicity.
The R-code for regression model is,
a=read.table("clipboard",header=F)
attach(a)
y=c(22.3,22.6,16.7,25.9 ,18.3 ,18.7,13.1,23.3,17.3,26.2,18.7,34.6,22.3,5.4,12.3,28.7)
x1=c(23.7,21.1,11,26.6,11.6,9.8,13.4,9.7,11.5,25.6,8.2,25.1,15.0,14.9,7.3,17.8)
x2=c(0.0,5.3,16.5 ,9.4,18.4 ,8.3,13.1,21.9 ,5.6 ,18.9,8.1,12.8,2.7,5.4,23.7,28.7)
x3=c(2,2,1,2,1,1,3,3,3,2,1,2,2,3,1,3)
l=lm(y~x1+x2+x3)
l
summary(l)
And the output is,
> l
Call:
lm(formula = y ~ x1 + x2 + x3)
Coefficients:
(Intercept) x1 x2 x3
7.3862 0.7585 0.2705 -1.1533
> summary(l)
Call:
lm(formula = y ~ x1 + x2 + x3)
Residuals:
Min 1Q Median 3Q Max
-11.2878 -2.6058 -0.3359 3.6475 7.0212
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 7.3862 5.3544 1.379 0.19292
x1 0.7585 0.2257 3.360 0.00567 **
x2 0.2705 0.1770 1.528 0.15250
x3 -1.1533 1.7995 -0.641 0.53363
---
Signif. codes:
0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 5.52 on 12 degrees of freedom
Multiple R-squared: 0.5006, Adjusted R-squared: 0.3758
F-statistic: 4.01 on 3 and 12 DF, p-value: 0.03435
Thus here linear model is given as follows:
Gross Sales
(P/Eratio) =(0.7585)profit + (0.2705) Growth -(1.1533)Industry +7.3862
margin
Interpritation:
1)Here adjusted R-squared is 0.3758 i.e. It explained 37% variation.
Thus it is not much adequate model.
2)F-statistics has value 4.01 on 3,12 degrees of freedom.
But the value of F(0.95,3,12) is 3.49029 which is less than calculated
F. Thus we reject our null hypothesis.
Now, Given Gross profit margin is 16% and Sales Growth is 13%.
The industry is not specified as which is oil industry.
We consider the oil industry given is 1.
Then
P/Eratio = (0.7585)*(16)+(0.2705)*(13)-(1.1533)+0.3862
= 14.8854
P/E ratio point estimate for a firm with
gross profit margin = 16% sales growth = 13%
operates in the oil industry is 14.8854
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