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	3

Answer 1

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