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MT230

MINITAB PROJECT SHEET 4 Question 1 Go back to the results from last week (the data are in the file Data for Project 3 on Moodle). (a) As in (c) last week, carry out the regression of Market share against all five variables (Delivery, Price, Image, Service and Product). Then remove variables Delivery and Product from the regression and use the other three. Use these results to calculate the partial F-statistic for two variables Delivery and Product given that the three other variables are already in the model (see Section 3.7.1). Now use Minitab to find the P-value and comment on the result. (b) Carry out the regression of Market share against variables Delivery, Price, Image and Service. Comment on the P-value of the T -test for the variable Delivery. Then remove Delivery from the regression and use the other three. As in (a), use these results to calculate the partial F-statistic for Delivery given that the three other variables are already in the model, and find the P-value. Compare the P-values for the partial F-statistic to that of the T -test for the variable Delivery. Comment on the result. (If your calculations are correct, you should obtain the same P-values for both tests. This is not a coincidence. It can be proved that these two tests are equivalent: the square of the T statistic is equal to the corresponding partial F-statistic, see Section 3.7.3). (c) Compare the P-values of the T -tests for the variable Service for the two regression models considered in (b). Any comments? Question 2 The data in the file Data - PEmax relate to ten sets of measurements which were made on each of twenty-five patients with cystic fibrosis. The response variable PEmax which signifies the severity of the condition is thought to be caused by several of the nine remaining variables. Carry out the regression of PEmax against three explanatory variables “age”, “FEV”, “RV”. Test whether the intercept can be taken zero. If so, refit the model and comment the result. (To fit a model with α = 0, use STATS/REGRESSION/ REGRESSION/FIT REGRESSION MODEL, click MODEL and uncheck the box ”include the constant term in the model”.) Question 3 Suppose that a laboratory study is undertaken to determine the relationship between the dosage (X) of a certain drug and weight (Y ). Eight laboratory animals of the same sex, age and size are selected and randomly assigned to one of eight dosage levels. The gain in weight (in dekagrams) is measured for each animal after a two-week time period during which all animals were subject to the same dietary regimen. The data are in the file Data - PolR on Moodle. Suggested procedure: Plot Y against X in a scatterplot to get an impression of the possible dependence. Then try adding new variables to see if you can model it successfully by a polynomial. This can be done using STATS/REGRESSION/ REGRESSION/FIT REGRESSION MODEL, click MODEL and select the required power in the dialog box ”terms through order”. You should discuss the validity of the model....