# Nonlinear Regression Models

** Nonlinear Regression Models **

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**Specific instructions for this assignment:**

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All data can be found in the file labeled Data for HW5.

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This is __NOT__ a group assignment; your submission should reflect __your__ work.

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Output from Stata (or software other than Excel) must be provided to earn any credit, and the values that you reference to answer any question must be highlighted in the output.

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If you are handing in multiple pages, please staple the pages together.

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For each problem that is a hypothesis test, make sure you: (1) specify the competing hypotheses, (2) show the value of the test statistic, (3) show the method by which you make a decision, and (4) answer the question! Your computer output should corroborate your findings.

1. (50 points) Access **Wages**. This is a cross-sectional data set on 526 working individuals. Estimate:

,

where *Wage* is in $ per hour, is years of schooling, and * *is years of working experience.

a.

(10 points) Predict the hourly wage of an individual with 15 years of education and 10 years of experience (be careful to make the correct adjustment!).

b.

(10 points) Interpret the coefficient attached to *Education*.

c.

(10 points) Are *Experience* and *Experience*^{2} jointly significant at the 5% level?

d.

(20 points) Is *Experience*^{2} statistically significant at the 5% level? Does it appear that the relationship between ln(Wage) and Experience is linear, U-shaped, or inverted U-shaped? If it is U-shaped or inverted U-shaped, then what is the value of *Experience* that minimizes or maximizes the ln(*Wage*)?

2. (50 points) Access **Buscost** which contains two variables describing the operation of 246 bus companies in U.S. cities. TC is the total operating expense of the company, in thousands of dollars; RVM is the total output of the firm, in thousands of revenue vehicle miles (miles driven by buses in service).

a.

Estimate the linear model: .

i. What is the estimated __marginal cost__ of providing one more RVM of output? (Make sure you report the correct units of measurement.)

ii. Interpret the coefficient of determination,

b.

Elasticity is equal to marginal cost, multiplied by output and divided by total cost.

i. What is the estimated elasticity of cost with respect to output when the firm produces 2 million RVM ? (Recall that RVM is measured in thousands.) You need to calculate the predicted value of total costs when RVM is 2 million.

ii. What is the estimated elasticity of cost with respect to output when the firm provides 5 million RVM? Is the elasticity constant or not?

c.

Estimate the log-log model: . What is the estimated elasticity of cost with respect to output when the firm provides 5 million RVM? Is the elasticity constant or not?

d.

In the log-log model, can you conclude that elasticity differs from one at the 5% significance level? Show all relevant steps.

e.

Can you compare the two values from the linear and the log-log models? Why or why not? If yes, which model provides a better fit? If not, then use the results from part (d) to calculate an value that can be compared to the from part (a). In terms of the value, which model provides a better fit (at the end round *R*^{2} to at least four decimal points)?