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Statistical Problems

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1.) Two candidates for governor participated in a televised debate. A political pollster recorded the preferences of 500 registered voters in a random sample prior to and after the debate:
Preference After Debate
Preference Prior Candidate A Candidate B Total
To Debate

Candidate A 269 21 290
Candidate B 36 174 210

Total 305 195 500

a. At the 0.01 level of significance, is there evidence of a difference in the proportion of voters who favored Candidate A prior to and after the debate?
b. Compute the p-value in (a) and interpret its meaning.

2.) Professional basketball has truly become a sport that generates interest among fans around the world. More and more players come from outside the U.S. to play in the NBA. You want to develop a regression model to predict the number of wins achieved by each NBA team, based on field goal (shots made) percentage for the team and for the opponent. The data is stored in the attached file: NBA2009.

a. State the multiple regression equation.
b. Interpret the meaning of the slopes in this equation.
c. Predict the number of wins for a team that has a field goal percentage of 45% and an opponent field goal percentage of 44%.
d. Perform a residual analysis on your results and determine whether the regression assumptions are valid
e. Is there a significant relationship between number of wins and the two independent variables (field goal percentage for the team and for the opponent) at the 0.05 level of significance?
f. Determine the p-value in (e) and interpret its meaning.
g. Interpret the meaning of the coefficient of multiple determination in this problem.
h. Determine the adjusted r2.
i. At the level of 0.05 level of significance, determine whether each independent variable makes a significant contribution to the regression model. Indicate the most appropriate regression model for this set of data.

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Statistical Problems

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Statistics Problems - Regression Analysis, Autocorrelation, Multicollinearity

1. Suppose an appliance manufacturer is doing a regression analysis, using quarterly time-series data, of the factors affecting its sales of appliances. A regression equation was estimated between appliance sales (in dollars) as the dependent variable and disposable personal income and new housing starts as the independent variables. The statistical tests of the model showed large t-values for both independent variables, along with a high r2 value. However, analysis of the residuals indicated that substantial autocorrelation was present.

a. What are some of the possible causes of this autocorrelation?

b. How does this autocorrelation affect the conclusions concerning the significance of the individual explanatory variables and the overall explanatory power of the regression model?

c. Given that a person uses the model for forecasting future appliance sales, how does this autocorrelation affect the accuracy of these forecasts?

d. What techniques might be used to remove this autocorrelation from the model?

2. Suppose the appliance manufacturer discussed in Exercise 1 also developed another model, again using time-series data, where appliance sales was the dependent variable and disposable personal income and retail sales of durable goods were the independent variables. Although the r2 statistic is high, the manufacturer also suspects that serious multicollinearity exists between the two independent variables.

a. In what ways does the presence of this multicollinearity affect the results of the regression analysis?

b. Under what conditions might the presence of multicollinearity cause problems in the use of this regression equation in designing a marketing plan for appliance sales?

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