A financial analyst engaged in business valuation obtained financial data on 71

Question

A financial analyst engaged in business valuation obtained financial data on

71

drug companies. Let Y correspond to the price-to-book value ratio,

Upper X1

correspond to the return on equity, and

UpperX2

correspond to the growth percentage. Use the accompanying data to complete parts a. through e. below.

Develop a regression model to predict price-to-book-value ratio based on return on equity.

ModifyingAbove Upper Y with caret Subscript iYiequals=nothing plus+nothing Upper X Subscript 1 iX1i

(Round to four decimal places as needed.)

Develop a regression model to predict price-to-book-value ratio based on growth.

Develop a regression model to predict price-to-book-value ratio based on return on equity and growth.

Compute and interpret the adjusted

r squaredr2

for each of the three models

Which of these three models do you think is the best predictor of price-to-book-value ratio?

Table

Price/Book Value Ratio Return on Equity Growth% 1.442 12.911 6.547 8.291 11.948 135.696 1.964 12.384 0.013 6.529 25.238 14.275 1.244 8.743 22.718 3.364 38.053 18.994 2.493 25.595 24.531 5.204 19.733 11.611 2.403 22.865 49.801 7.614 69.766 36.819 0.527 3.767 41.131 2.517 9.175 28.865 7.559 29.134 52.095 5.117 17.679 25.225 2.025 29.278 23.909 4.854 31.377 9.593 2.122 14.799 18.433 4.154 12.003 39.032 1.986 14.152 39.507 1.513 14.114 27.106 2.003 14.998 13.171 5.032 20.525 17.186 2.295 14.862 15.865 2.088 5.602 16.805 2.832 11.207 8.394 1.748 16.094 18.323 5.489 23.913 16.801 4.565 14.714 46.448 2.456 6.306 34.045 1.588 19.043 8.439 8.364 38.985 15.052 2.233 15.142 25.192 2.877 19.786 0.343 7.364 18.442 3.275 3.352 20.745 9.456 2.832 34.642 7.056 2.402 15.578 9.464 1.185 10.373 4.697 3.005 23.487 4.113 10.165 91.556 13.366 2.124 1.634 15.931 1.642 9.439 5.783 2.079 19.424 0.105 7.188 4.941 102.747 1.304 42.678 1.537 5.715 90.882 74.063 6.386 19.439 8.899 2.638 27.296 34.573 3.474 12.966 12.166 6.886 24.648 11.554 13.583 81.874 24.615 4.077 1.449 20.097 7.181 3.686 22.264 6.136 31.503 49.821 1.011 4.984 13.312 9.366 47.757 61.216 1.327 13.441 10.814 1.041 36.047 9.025 3.772 28.757 71.116 3.619 18.166 51.822 2.283 14.063 17.061 10.082 133.115 171.403 4.298 21.851 8.593 8.467 11.345 247.709 2.063 17.351 10.839 4.141 19.473 6.464 2.317 8.449 24.496 2.986 18.676 14.194 4.507 21.625 5.858 5.115 49.517 31.451 2.106 19.384 3.856

Explanation / Answer

we will analyse this using the open source statistical package R , the complete snippet is as shown below

# read the data into R dataframe
data.df<- read.csv("C:\Users\586645\Downloads\Chegg\equity.csv",header=TRUE)

### fit a model , with equity as the dependent variable

fit <- lm(Ratio~ Equity, data=data.df)

## the results of the model are
summary(fit)

### fit a model , with growth as the dependent variable

fit1 <- lm(Ratio~ Growth, data=data.df)

## the results of the model are
summary(fit1)

### fit a model , with growth and equity as the dependent variable

fit2 <- lm(Ratio~ Growth + Equity, data=data.df)

## the results of the model are
summary(fit2)

The results are

> summary(fit)

Call:
lm(formula = Ratio ~ Equity, data = data.df)

Residuals:
Min 1Q Median 3Q Max
-4.0165 -1.5955 -0.6384 1.3431 5.5201

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 2.33450 0.38397 6.080 5.90e-08 ***
Equity 0.06997 0.01167 5.994 8.34e-08 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.197 on 69 degrees of freedom
Multiple R-squared: 0.3424, Adjusted R-squared: 0.3329
F-statistic: 35.93 on 1 and 69 DF, p-value: 8.343e-08

summary(fit1)

Call:
lm(formula = Ratio ~ Growth, data = data.df)

Residuals:
Min 1Q Median 3Q Max
-3.8722 -1.6221 -0.5825 1.2020 9.6932

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 3.130733 0.357162 8.766 7.98e-13 ***
Growth 0.030839 0.007341 4.201 7.82e-05 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.418 on 69 degrees of freedom
Multiple R-squared: 0.2037,   Adjusted R-squared: 0.1921
F-statistic: 17.65 on 1 and 69 DF, p-value: 7.818e-05

summary(fit2)

Call:
lm(formula = Ratio ~ Growth + Equity, data = data.df)

Residuals:
Min 1Q Median 3Q Max
-3.575 -1.434 -0.560 1.177 6.196

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.945989 0.375822 5.178 2.17e-06 ***
Growth 0.021804 0.006446 3.383 0.00119 **
Equity 0.059898 0.011277 5.311 1.30e-06 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 2.048 on 68 degrees of freedom
Multiple R-squared: 0.4372, Adjusted R-squared: 0.4206
F-statistic: 26.41 on 2 and 68 DF, p-value: 3.26e-09

The value of r2 basically explains the percentage of variation captured by the model , higher the value better the model. The r2 value is highest when both growth and equity are used as independent variables to prdict the price book ratio . Adjustedr2 is same as r2 except that the model is penalised for using more predictors . it is a conservative figure for r2 value but the interpretation is same. (Higher the value better the model)

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