ECMT2150 - Intermediate Econometrics - Probability & Statistics Simple and Multiple Linear Regression - Report Writing Assignment Help

ECMT2150 Probability & Statistics Simple and Multiple Linear Regression Intermediate Econometrics  Report Writing Assignment Help

Assessment Task:

Question 1

X and Y are discrete random variables with the following joint distribution:

That is, Pr (X =1, Y=1) = 0.02 and so forth. Report answers rounded to 2 decimal places.
i. Compute the following probabilities:
a. Prob[Y<2]
b. Prob[Y<2,X>5]
ii. Find the marginal probability density functions for X and Y.
iii. Calculate the mean, standard deviation, and variance of Y.
iv. Calculate the conditional probability density function, mean, standard deviation,
and variance of Y given X = 5.
v. Calculate the covariance and correlation between X and Y.
vi. Are X and Y independent? Explain.

Question 2
In a study relating marks obtained by students in undergraduate econometrics units (metric) in Australian universities to time spent in various activities, a survey is conducted among several students. The students are given questionnaires and are asked to write how many hours they spend each week in four activities: studying, sleeping, working and leisure. Any activity is put into one of the four categories, so that for each student, the sum of hours in the four activities must be 168.

i. In the model

metric = β0 + ββ1study + ββ2sleep + ββ3work + ββ4leisure + u,
does it make sense to hold sleep, work and leisure fixed, while changing study?
ii. Explain why this model violates Assumption MLR.3.
iii. How could you reformulate the model so that its parameters have a useful
interpretation and it satisfies Assumption MLR.3?

Question 3
The following table contains data taken from 10 countries, showing their wine consumption per capita (ALCOHOL) and number of deaths from liver disease per 100,000 persons (DEATHS).

Answer the questions below using either a calculator or EXCEL and show your work. Do not use STATA.
i. Estimate the relationship between DEATHS and ALCOHOL using OLS; that is, obtain the intercept and slope estimates in an OLS regression of DEATHS on ALCOHOL.
ii. Comment on the direction of the relationship between DEATHS and ALCOHOL.
Does the intercept have a useful interpretation here? Explain. How much higher is DEATHS predicted to be if ALCOHOL is increased by five units?
iii. Compute the fitted values and residuals for each observation and verify that the residuals (approximately) sum to zero.
iv. What is the predicted value of DEATHS when ALCOHOL = 5?
v. How much of the variation in DEATHS for these 10 countries is explained by ALCOHOL? Explain.

Question 4: Empirical Exercise Using Stata

The data file nbasal.dta contains salary information and career statistics for a sample of 269 NBA players. In this exercise, you will investigate how salaries are related to
basketball player’s minutes played.
i. Compute the mean and standard deviation of player’s average minutes per game played (avgmin) and annual salary (wage).
ii. Construct a scatterplot of people’s wages on minutes played. Does therem appear to be a relationship between the variables?

A model that relates player’s wages to their average minutes played per game is:

wage = βo + β1avgmin + u

iii. Estimate the model. Report the results in equation form, including the sample size, R-squared, and adjusted R-squared. Interpret the intercept and comment on whether its estimate provides any useful information.
iv. Comment on the direction and size of the regression’s slope. Does the estimated effect of player’s minutes per game played on their wages have the sign you expected? Why? Is the estimated relationship between minutes played and wages large or small? Explain what you mean by “large” and “small”.
v. Suppose Player X has an average value of avgmin, while Player Y’s value of avgmin is one standard deviation above the average. Predict Player X and Player Y’s wage.
vi. Based on the estimated value of RR2 interpret the goodness-of-fit of the estimated regression model. Does avgmin explain a large fraction of the variation in wages across persons? Explain.
vii. Re-estimate the model taking players’ other performance statistics; average points scored (points), average rebounds (rebounds), and average assists
(assists) into account. Report the new results in equation form, including the sample size, R-squared, and adjusted R-squared. How does accounting for a
player’s average game performance change your regression results? Comment on which performance indicator appears to be most valued in the NBA.
viii. What is the correlation between avgmin and points? Does this pose a problem for OLS regression?

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