How To Predict A Team'S Winnings

Transcription

1 THIS PAPER IS NOT TO BE REMOVED FROM THE EXAMINATION HALLS University of London BSc Examination 2012 BA1040 (BBA0040) +Enc Business Administration Business Statistics Date tba: Time tba DO NOT TURN OVER UNTIL TOLD TO BEGIN Time allowed: TWO hours Answer FOUR Questions All questions carry equal marks Electronic calculators may be used. These should be of a hand-held non-programmable (where relevant) type and the name and model should be stated CLEARLY on the front of your answer book. Appropriate statistical tables are attached, you may not necessarily need to use them all. PLEASE TURN OVER University of London 2012 UL12/ 1 of 6

2 Question 1: a) What is the difference between sampling with replacement and without replacement? Give an example. b) What is the difference between probability and non-probability sampling? Give an example c) In regression analysis, what is meant by the method of least squares? d) What are the differences between a Type I error and a Type II error? Give an example. e) What is the difference between parametric and non-parametric statistical methods? Give an example. Sub-Total: 2 Page 2 of 6

3 Question 2: Crazy Dave, a well-known baseball analyst, wants to determine which variables are important in predicting a team s wins in a given season. He has collected data related to wins, earned run average (ERA), and runs scored for the 2008 season (see below): Team League Wins E.R.A. Runs Scored Hits Allowed Walks Allowed Saves Errors Baltimore Boston Chicago White Sox Cleveland Detroit Kansas City Los Angeles Angels Minnesota New York Yankees Oakland Seattle Tampa Bay Texas Toronto Arizona Atlanta Chicago Cubs Cincinnati Colorado Florida Houston Los Angeles Dodgers Milwaukee New York Mets Philadelphia Pittsburgh St. Louis San Diego San Francisco Washington Page 3 of 6

4 Below is the excel output of the model developed to predict the number of wins based on ERA and runs scored: Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 30 ANOVA df SS MS F Significance F Regression E-12 Residual Total Coefficients Standard t Stat P-value Error Intercept E-07 E.R.A E-10 Runs Scored E-09 a) State the multiple regression equation for the above model (define your Y and X values clearly) b) Interpret the meaning of the slopes in this equation. c) Predict the number of wins for a team that has an ERA of 4.50 and has scored 750 runs. d) Is there a significant relationship between number of wins and the two independent variables (ERA and runs scored) at the 0.05 level of significance? e) Interpret the R square statistic above. 3 marks f) Why would the adjusted R-square be superior to the R-square? 2 marks Sub-Total 2 Page 4 of 6

5 Question 3: A survey conducted by the National Post entitled send your infants to nursery reports that children (aged 3 months 5 yrs) that attend a play group or nursery scheme three or more mornings a week achieve higher academic levels in subsequent years than those who were kept at home or babysat in a relatives or friend s home. a) What information would you want to know before you accepted the results of this survey? 12 marks b) Assume you are in charge of this study. Briefly explain how you would organise this research exercise. You should mention something about the sampling frame, the sampling method, the survey questions, and the hypotheses you would test. 13 marks Sub-Total: 2 Question 4: The following data represent total revenues (in millions of constant 2000 pounds) by a car rental agency over the 11-year period between 2000 and 2005: 4.0, 5.0, 7.0, 6.0, 8.0, 9.0, 5.0, 2.0 a) Compute the 3 year moving averages for this annual time series. b) Plot the original figures and the (MA(3)) figures in a rough diagram and use it to discuss the trend. c) Interpret your results in simple management terms. d) What other method(s) could you use to forecast the figures for e) Explain what is meant by the Classical Multiplicative Time-Series Model. How and why would one want to deseasonalise a variable? Sub-Total 2 5 of 6

6 Question 5: A survey was conducted for drivers of Sedans in 2009 on fuel consumption. The overall results per gallon (MPG) of 2009 Sedans priced under 20,000 are as follows: 27; 31; 30; 28; 27; 24; 29; 32; 32; 27; 26; 26; 25; 26; 25; 24 a) Compute the mean, median and mode 3 marks b) Compute the variance c) Compute standard deviation d) Compute range e) Compute the coefficient of variation f) Are the data skewed? If so how? 2 marks Sub-Total: 2 Question 6: Approximately 5% of US families are millionaires (i.e. have a net worth in excess of $1 million). However, 30% of Microsoft s employees are millionaires. If random samples of 100 Microsoft employees are selected, what proportion of the sample will have? a) between 25% and 35% millionaires? b) between 20% and 40% millionaires? c) more than 40% millionaires? d) If samples of size 50 are taken, how does this change your answers to (a)-(c)? e) Explain intuitively why the normal distribution which is a continuous distribution can be used to make inferences about a dichotomous random process (such as the one described above). Sub-Total: 2 END OF PAPER Page 6 of 6