Regression Analysis

Part 1. Use worksheet “baseball stats” to perform a multiple regression analysis on the dataset found in BB2011 tab, using Wins as the dependent variable, and League, ERA, Runs Scored, Hits Allowed, Walks Allowed, Saves, and Errors as candidates for the independent variables. Perform the analysis at the 5% significance level.
a) Create a full write up, where you write your statistical analysis step by step. In your write up, make sure you address the following points.
• Methodology and steps that you took to get to your final regression equation.
• Final regression equation output.
• What is the final regression equation?
• Interpret all the coefficients in the equation.
• Speak to whether the signs on the coefficients make sense.
• Interpret R squared.
• Include a full residual analysis.
• What is the residual of the Tampa Bay observation?
b) Now, use tab BB2012 to make predictions of wins in 2012, using the model you created with the 2011 stats.
• How many games are the Giants (SFG) expected to win in 2012?
• Which team is predicted by the model to have the worst record in 2012?
• Which team is predicted by the model to have the best record in 2012?

Part 2. Use the CocaCola data set to analyze quarterly data on Coca Cola’s revenues.

a. Plot the time series as a line graph. Make sure the graph is polished enough to be included in a formal report – i.e. it has a good title, axis titles/formatting, etc. (if you can, format the x-axis to have years and quarters)
b. Perform a regression using seasonal binaries. Use 0.1 level of significance for eliminating p-values. Include the final output and write the final regression equation.
c. Plot the fitted values of your time series on the same graph as the actuals. Does your regression look good?
d. Interpret the results. Make sure to talk about seasonality.
e. Use the regression equation to make a prediction for each quarter in 2011.

Part 3. Bob analyzed water damage claims filed at a small Louisiana home insurance company over the last 15 years. He fitted several different trend models, shown below. Which trend model seems most reasonable (or more than one) for making forecasts for the next three years? What about the principle of Occam’s Razor?