Statistics - Regression Projects

The controller’s office in the government of the state of Mississippi would like to estimate the amount

The controller’s office in the government of the state of Mississippi would like to estimate the amount turned over to the state government as profit once a proposed lottery has been operating for at least one year. The following information is available from a recent year from 23 states. The data are given in file quiz3.xls which you have obtained from the instructor.
1. How do we determine if it makes sense to use linear regression in this situation? Does it make sense to use linear regression here? Why?
2. What is the estimated linear model for predicting lottery profit?
3. Interpret the slope coefficient in the estimated equation for predicting profit in the context of this example.
4. Interpret the intercept coefficient in the estimated equation for predicting profit in the context of this example.
5. According the estimated model, is there a significant linear relationship between profit and sales? Explain.
6. How strong is the linear relationship between profit and sales? Interpret this number in the context of the problem.
7. If sales were to increase by $1 million, construct and interpret the 99% confidence interval for the estimated change in profit in this case.
8. If Mississippi sales were $120 million, construct and interpret a 95% interval estimate for the amount of money provided to the state government.
Basketball is a popular sport throughout the world. Data from the 2006 season for all 30 teams of the National Basketball Association (NBA) is given on the following variables: Variables:
Wins = number of wins in the season (all teams play 82 games)
Field Goal % = percentage of shots made (except for free throws)
Field Goal % Allowed = percentage of opponents shots made (except for free throws) Own Turnovers = average number of turnovers per game
Opponent Turnovers = average number of turnovers by opponent in a game
Offensive Rebound % = percentage of rebounds obtained on the offensive end of the court Defensive Rebound % = percentage of rebounds obtained on the defensive end of the court
The data in file quiz3.xls that you will obtain from your instructor.
Glossary:
• During play, each shot taken by the team with the ball is called a "field goal".
• Free Throws (which are not included in field goal percentage) are free shots awarded because of fouls.
• A turnover is when the team makes a mistake and gives the ball to the other team.
A rebound occurs on a missed field goal attempt, when a team obtains the ball after the missed shot.
A defensive rebound occurs when a team with the ball misses the shot and the other team gets the ball.
An offensive rebound occurs when a team with the ball misses the shot and they get the ball back.
Estimate the following two models:
Model A: Predict Wins using all other variables as independent variables.
Model B: Predict Wins using ONLY Field Goal %, Field Goal % Allowed and Own Turnovers
1. What is the most highly correlated variable with "Wins"? What is the correlation?
2. Write the estimated regression equation (Model A) that predicts number of "Wins" as a function of all the other variables.
3. Interpret the estimated coefficient of "Opponent Turnovers" Model A. Does the sign of the slope coefficient make sense in the context of this problem? Explain.
4. What variable has the biggest effect on "Wins" in Model A? What is t he effect (in words)? Does that surprise you? (Explain)
5. Is Model A a significant model overall? Justify your answer.
6. Which of the independent variables in Model A are significant at the 10% level?
7. Construct and interpret a 99% confidence interval for the estimated effect on "Wins" when a team’s own "Field Goal %" is increased by 1 % based on Model A.
8. Is Model B statistically as good as Model A? Justify your answer in the best way possible.