For this exercise, you will be using a variation of NBASAL, which contains cross$-$sectional data on NBA basketball player performance and characteristics such as the number of years as a professional player, position, and other basketball statistical variables.

The following section gives detailed information about the variables within the data set:

Variable Descriptions

marrmarr$=1,$ if the player is married, and $0$ otherwise;wagewage$=$ annual salary, in thousands of dollars;experexper$=$ years as professional player;ageage$=$ age, in years;collcoll$=$ years played in college;gamesgames$=$ average games played per year;minutesminutes$=$ minutes played per season;guardguard$=1,$ if the player is a guard, and $0$ otherwise;forwardforward$=1,$ if the player is a forward, and $0$ otherwise;centercenter$=1,$ if the player is a center, and $0$ otherwise;pointspoints$=$ points scored per game;reboundsrebounds$=$ rebounds per game;assistsassists$=$ assists per game;draftdraft$=$ draft number;allstarallstar$=1,$ if the player has ever been an All$-$Star, and $0$ otherwise;avgminavgmin$=$ average minutes played per game;lwagelwage$=$ log$($wage$)$logwage;blackblack$=1,$ if the player is black, and $0$ otherwise;childrenchildren$=1,$ if the player has children, and $0$ otherwise;expersqexpersq$=$ exper$2$exper$2$;agesqagesq$=$ age$2$age$2$;marrblckmarrblck$=$ marr$$blackmarr$$black.

Open any of the following data files to reference the data from NBASAL$\_$V$5.$ Use the chosen data file to answer each of the following questions.

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Open R File

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Open Excel File

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Open Stata File

$($i$)$

Estimate a linear regression model relating points per game to experience in the league and position $($guard$,$ forward, or center$).$ Include experience in quadratic form and use centers as the base group.

The estimated equation is points$$points$^==+$experexper$+$exper$2$exper$2+$guardguard$+$forwardforward$.$

$($ii$)$

The dummy variables for all three positions are not$$included in part $($i$)$ because:

Including the dummy variables for all three positions would result in the dummy variable trap.

Many players in the data set are guards.

Very few players in the data set are centers.

The number of dummy variables cannot exceed the number of quantitative variables.

$($iii$)$

Holding experience fixed, a guard scores roughly$$points per game than a center, holding experience fixed.

True or False: The difference between a guard score and a center score is statistically significant at the $5\%$ significance level against a two$-$sided alternative.

True

False

$($iv$)$

Now add marital status to the equation.

The estimated equation is points$$points$^==+$experexper$+$exper$2$exper$2+$guardguard$+$forwardforward$+$marrmarr$.$

Holding position and experience fixed, it$$be concluded that married players are more productive than unmarried players based on points per game at the $5\%$ significance level.

$($v$)$

Add interactions of marital status with both experience variables.

The estimated equation is points$$points$^==+$experexper$+$exper$2$exper$2+$guardguard$+$forwardforward$+$marrmarr$+$marr$$expermarr$$exper$+$marr$$exper$2$marr$$exper$2.$

In this expanded model, there$$strong evidence that marital status affects points per game at the $5\%$ significance level, as the F$$statistic for the joint significance of the variables marrmarr, marr$$expermarr$$exper$,$ and marr$$exper$2$marr$$exper$2$is approximately$$with p$-$value equal to$.$

$($vi$)$

Estimate the model from part $($iv$),$ but use assists per game as the dependent variable.

The estimated equation is assists$$assists$^==+$experexper$+$exper$2$exper$2+$guardguard$+$forwardforward$+$marrmarr$.$

True or False: Holding position and experience fixed, it cannot be concluded that married players are more productive in the number of assists per game than unmarried players at the $5\%$ significance level.

True

False

There is relatively more evidence that married players are more productive than unmarried players in the number of$$per game.

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