C291FE2012_FinalVersion_Apr9

# 2813 you may use mathematical expressions or as

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a) What are the null and alternative hypotheses that are tested by the F-stat of 5.2813? You may use mathematical expressions or as sentences, but be clear and precise. H 0 : H a : b) Using a 5% significance level, what is the critical value (F*) for the F-stat? c) What is your conclusion from the F-test? Be clear and concise; use one sentence only. d) Based on this output, which variable(s), if any, do you think could be safely deleted from the model, without much loss of explanatory power? Circle all your choices. AGE EXPERIENCE DEGREES PREVJOBS 16

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e) What is the estimated difference in salary ( in dollars) between two employees where one is 10 years older than the other, but who in other respects are identical (i.e. same experience, number of degrees and number of previous jobs). Remember to convert from \$1000s to \$s. f) What percentage of the total variation in Salary is explained by this full model with four predictor variables? Report to the nearest whole number. g) What would be the most likely effect on R 2 if PREVJOBS were dropped from the model? It would increase It would decrease It would not change h) What would be the most likely effect on R 2 if the sample size were doubled? It would increase It would decrease It would not change i) If you dropped two of the predictor variables, and fit a new model, then the degrees of freedom (numerator, denominator) for the new F-stat would be: __ A. 2, 15 __ B. 2, 17 __ C. 2, 19 __ D. 1, 17 __ E. 1, 19 j) In multiple regression, if the model provides a poor fit, this indicates that: __ A. The Sum of Squares Error will be large __ B. The Standard Error of predictions will be large __ C. The R Square will be close to 0 __ D. All of the above 17
Question 9. (Total 6 marks) “This vegetable question has a ‘getable’ answer” A health food company wants to determine the best process for blanching dark green vegetable material so it can be added to other food products without losing vitamin A. They examine three different processes to determine which is best in terms of vitamin A retention (mg/100mg). The data collected and partial ANOVA results appear below. Process 1 Process 2 Process 3 60 45 50 58 40 52 55 35 56 62 34 47 68 52 48 52 49 52 64 48 51 66 39 50 SUMMARY Groups Count Sum Average Variance Process1 8 485 60.625 29.982 Process2 8 342 42.750 45.071 Process3 8 406 50.750 7.643 ANOVA Source of Variation SS df MS F P-value Between Groups 1282.750 2 Within Groups 578.875 21 Total 1861.625 23 a) Write the null and alternative hypotheses. H 0 : _________________ H a : _________________ b) The F statistic value is: __ A. 23.267 __ B. 2.216 __ C. 27.565 __ D. 7.924 __ E. Cannot be determined from the given information c) The P -value for this statistic is less than 0.001. Therefore, at α = .05: __A. Reject the null hypothesis, and conclude that the variances across the three processes are not all equal. __B. Reject the null hypothesis, and conclude that all three processes have different mean retention amounts. __C. Reject the null hypothesis, and conclude that mean retention amounts are not all equal across the different processes.

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