Question
Profit Forecasting: A company is interested in predicting profit for a number of projects based on two explanatory variables: a measure of risk assigned at
Profit Forecasting:A company is interested in predicting profit for a number of projects based on two explanatory variables: a measure of risk assigned at the outset of the project (x1= RISK) and the expenditure on research and development for the project (x2= RD). Data on the three variables PROFIT, RISK, and RD are available in the worksheet entitledRD5.PROFITis measured inthousands of dollarsandRDis measured inhundreds of dollars. Use the data to fit two separate regression models.
For the first model (Linear Model AKA First Order Model), regress PROFIT on the two explanatory variables RISK and RD. (Hint: "Regress PROFIT onx" implies that PROFIT is theyvariable andxis the explanatory variable.)
a) State thelinearmodel equation.
=0+1(1
x1
) +2x2
=0+1x1+2(1
x2
)
=0+1x1+2x2+3x22
=0+1x1+2x2
=0+1x1+2x12+3x2
However, there is some evidence that the relationship between RD and PROFIT is nonlinear. Therefore, next fit the second order polynomial regression model, regress PROFIT on RISK, RD, and RDSQR (the square of the RD variable) as explanatory variables. (Hint: You will have to create the RDSQR variable yourself.)
b) State thetransformedmodel equation (i.e., the second order polynomial regression model equation).
=0+1x1+2(1
x2
)
=0+1x1+2x12+3x2
=0+1x1+2x2
=0+1(1
x1
) +2x2
=0+1x1+2x2+3x22
c) Provide summary measures about the two models. (Enter yourR2values as percents to two decimal places and enter your standard errors to three decimal places.)
ModelR2R2adjseLinear Model%%Second-Order Model%%
d) Choose the model you prefer for PROFIT and provide a justification for your choice.
The first-order model is better because theR2adjis higher and the standard error is lower.
The second-order model is better because theR2adjis higher and the standard error is lower.
The first-order model is better because theR2adjis lower and the standard error is higher.
The second-order model is better because theR2adjis lower and the standard error is higher.
Regardless of your decision above, use theSecond Order Modelto answerALLof the questions below.Also, be sure to compute these values based on theUNROUNDED values in EXCEL.
e) Predict the profit for a project with a risk of 6.0 and a research and development expenditure of $9,000. (Enter your answers to two decimal places.)
$
f) Parts f) and h) require the use of partial differentiation. If you have forgotten how to, please re-watch the Tan Chapter 8, Part 2 video for a reminder. How quickly is the average profit increasingwith respect to riskfor a project with a risk of 6.0 and a research and development expenditure of $9,000? (Enter your answer to two decimal places.)
$
How quickly is the average profit increasingwith respect to research and development expenditurefor a project with a risk of 6.0 and a research and development expenditure of $9,000? (Enter your answer to two decimal places.)
$
g) Predict the profit for a project with a risk of 8.5 and a research and development expenditure of $6,000. (Enter your answers to two decimal places.)
$
h) How quickly is the average profit increasingwith respect to riskfor a project with a risk of 8.5 and a research and development expenditure of $6,000? (Enter your answer to two decimal places.)
$
How quickly is the average profit increasingwith respect to research and development expenditurefor a project with a risk of 8.5 and a research and development expenditure of $6,000? (Enter your answer to two decimal places.)
Data shown below:
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Analysis for Financial Management
Authors: Robert c. Higgins
8th edition
73041807, 73041803, 978-0073041803
