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Concordia Univ. BSTA 378 Assignment 2 Fall 2014

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Question 1;The following data set represents the sales of new cars by quarter from the first quarter of 2009 to the fourth quarter of 2012;Season Sales;First quarter 2009 97;Second quarter 2009 142;Third quarter 2009 108;Fourth quarter 2009 135;First quarter 2010 120;Second quarter 2010 164;Third quarter 2010 126;Fourth quarter 2010 150;First quarter 2011 123;Second quarter 2011 151;Third quarter 2011 141;Fourth quarter 2011 142;a)Derive a linear model to predict Sales. Describe the model. Calculate the corresponding Mean Absolute Deviation. Predict Sales for the first quarter of 2012.;b)Derive a model to predict Sales using linear trend and seasonality using dummy variables. Use the Best Subset selection approach with? = 0.05. Calculate the corresponding Mean Absolute Deviation. Predict Sales for the first quarter of 2012.;c)Consider a Three-Period Moving Average Forecasting model. Calculate the corresponding Mean Absolute Deviation. Predict Sales for the first quarter of 2012.;d)Consider a Three-Period Weighted Moving Average Forecasting model, where the highest weight (3) is given to the most recent data and the smallest weight (1) is given to the oldest data and (2) to the intermediate data. For example;?WMA?_t=(3*?SALES?_(t-1)+?2*Sales?_(t-2)+?1*Sales?_(t-3))/6;Calculate the corresponding Mean Absolute Deviation. Predict Sales for the first quarter of 2012.;e)Consider a two-period lagged variable model to predict Sales. Describe your final model where all the coefficients are significant. Calculate the corresponding Mean Absolute Deviation. Predict Sales for the first quarter of 2012.;f)Which model is better?;Question 2;A large university is interested in comparing the salaries of its graduate in the following areas: Business, Education, Engineering and Liberal Arts. The starting salaries of 22 students were recorded;Business Education Engineering Liberal Arts;14.5 12.2 24.7 10.6;22.4 11.4 25.6 14.7;24.1 12.8 26.7 15.2;21.7 11.7 24.9 12.1;17.9 12.5 28.7;18.1 30.1;20.2;a)Is there a significant difference in the population average salaries for the four areas of concentration? Use? = 0.05.;b)Find a 95% confidence interval for the difference between the Business and Engineering mean salaries.;c)Use a 95% Bonferroni family of confidence intervals to identify which pair(s) of means is(are) significantly different.;d)Use the Tukey method to identify which pair(s) of means is(are) significantly different. Use?=0.05.;e)Is the assumption of equal variances satisfied?

 

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