Dataset NBASAL contains a sample of NBA players: Wage =annual salary, thousands$ Lwage =natural log of

Dataset NBASAL contains a sample of NBA players:

Wage =annual salary, thousands$

Lwage =natural log of wage

Exper =years as a professional player

Draft= draft number (lower draft number is the more sought after player. For example, Lebron James and Kobe Bryant were #1 and #13 draft picks, respectively, during their years)

Guard =1 if player position is guard

Forward =1 player position is if forward

Center =1 player position is if center

Points =points per game

Rebounds =rebounds per game

Assists =assists per game

NOTE: All logs are natural logs.

You are interested in the relationship between the NBA player salary and the following two variables: exper and draft .

The relationship between NBA salary and years as a professional player can be described as "playing for NBA 1 additional year would increase the player salary by a certain percent." Write the simple linear regression model depicting the relationship between NBA player salary and exper.
You believe the effect of exper on lwage is diminishing as the player stays in the league longer. Write the simple linear regression model depicting the relationship between lwage and exper .
Consider the following model:
1. Lwage = beta not + beta 1 draft + beta 2 exper + u
What signs do you expect the slope coefficient be for each explanatory variable?
Run this regression model and present your parameter estimates in equation form.
Interpret the slope coefficients of each explanatory variable from your equation.
Holding exper constant at its average, what is the difference in NBA player salary between a player whose draft number was #15 and one who was #20? How do you interpret this difference?
Use the information on SST, SSE, and SSR (Remember this is sum square residual), what percentage of the variation in player salary is explained by exper and draft in model (1)?
What is the 90% confidence interval on exper ? How do you interpret this range?

9. There are only 3 possible positions a player can take—guard, center and forward. The dataset includes indicators on which position the player takes. If we include all 3 variable in our first model, which Gauss-Markov assumption would be violated?

10. Under this model, what is the effect of 1 additional year of experience on NBA salary for a player who has played in NBA for 5 years? For 10 years? What does it say about the effect of experience on salary?

Solution: With the aid of Minitab we find:

The multiple regression equation is given by:

\[\text{lwage}=5.5531+0.00003691\text{ draft}+0.14570\text{ exp}-0.006289\text{ ex}{{\text{p}}^{2}}\]

The variation in the logarithm of the salary when the experience increases in 1 year is equal to

\[\tilde{\Delta }=0.14570-0.006289\left( 2\exp +1 \right)=0.139411-0.012578\exp \]

For 5 years :
\[\tilde{\Delta }=0.139411-0.012578\times 5=0.076521\]
This means that
\[\log \left( \frac{{{S}_{1}}}{{{S}_{2}}} \right)=0.076521\Rightarrow {{S}_{1}}={{e}^{0.076521}}{{S}_{2}}=1.079525\]
In other words, the difference of salary is found as:
\[\Delta ={{S}_{1}}-{{S}_{2}}=0.079525{{S}_{2}}\]
This means that the salary increases a 7.9525%.
For 10 years :

\[\tilde{\Delta }=0.139411-0.012578\times 10=0.013631\]

This means that

\[\log \left( \frac{{{S}_{1}}}{{{S}_{2}}} \right)=0.076521\Rightarrow {{S}_{1}}={{e}^{0.013631}}{{S}_{2}}=1.013724\]

In other words, the difference of salary is found as:

\[\Delta ={{S}_{1}}-{{S}_{2}}=0.013631{{S}_{2}}\]

This means that the salary increases a 1.363%.

This suggests that exper has more influence in the salary, but this influence decreases as the experience is longer.

11. Compare the standard error of Beta 2 from model (1) and (2), how do you explain the difference?

12. Perform the statistical test that allows you to say whether exper and expersq are jointly statistically significant at 5% level.

13. You want to know that conditional on draft number and number of years playing in NBA, whether performance measures (such as number of rebound, points per game, and number of assists) affect the salary. What regression models would you run?

14. State and test the null hypothesis for question 12.

15. What is the difference between population regression line and simple regression line?

16. How does the residual differ from the error term in regression models?

17. Comment on what happens when the following Gauss-Markov assumptions got violated in the multiple regression models:

18. What is the difference between an economic model and an econometrics model?

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Solution: The downloadable solution consists of 17 pages, 1332 words and 10 charts.
Deliverable: Word Document