STA2201s06 Assignment 8
The file rest.dat contains the following variables for a sample of restaurants. We will pretend that all the variables are measured without error.
Let's fit a model in which the first four variables (basically representing restaurant size and advertising expenditures) are exogenous variables that are all related to one another. There is a straight arrow running from each exogenous variable to Sales, and another arrow from Sales to Capital improvement expenditures. There are arrows from both Sales and Capital improvement expenditures to Outlook.
One more arrow is in question, an arrow directly from Advertising expenditures to Outlook. That arrow is present in the full model, and absent in the reduced model. If the coefficient on that arrow is non-zero, it suggests that the management consultants may be directly influenced by advertising, and this would have some entertainment value.
Please conduct two tests of the null hypothesis. The Wald test will appear directly on the output as a t statistic. Please circle it on your printout and indicate whether you reject H0 at the 0.05 level. Also do a likelihood ratio test; make proc iml calculate the test statistic and the p-value. Circle them on the printout. Are the results of the two tests consistent with one another? What do you conclude about the management consultants?
If you are on Fisher and you do not want to deal with the data as they appear below, you can type (at the unix prompt)
cp /dos/brunner/public_html/2201s06/data/rest.dat .
The period is important; it refers to your current directory.
The first line of the data file consists of labels for the variables. SAS cannot use these, but it can ignore them. My SAS program includes the line
infile 'rest.dat' firstobs=2;
So the first observation starts on line 2.
ID# FT.EMPL PT.EMPL SEATS AdvExp CapExp SALES OUTLOOK 1 8 30 200 10 0 480 2 2 6 25 150 25 112 507 4 3 0 17 46 6 53 210 5 4 2 13 28 2 0 246 5 5 . . 44 1 0 148 2 6 2 . 50 5 0 50 3 7 0 5 50 4 0 72 2 8 1 8 130 1 7 99 3 9 2 10 . 0 8 160 4 10 2 19 50 5 17 243 4 11 3 12 64 4 6 200 4 12 30 40 240 100 200 1000 4 13 10 19 111 0 0 350 4 14 6 16 125 11 0 550 3 15 4 28 120 50 50 500 3 16 13 47 . 0 88 1100 4 17 7 15 92 17 0 416 3 18 20 25 90 33 0 650 2 19 1 16 150 3 0 292 5 20 15 10 90 20 40 400 3 21 0 0 15 0 0 42 3 22 0 7 80 1 15 100 2 23 0 10 76 0 0 75 4 24 1 14 65 4 0 180 3 25 0 20 178 6 0 201 4 26 7 13 110 27 164 273 6 27 51 80 60 0 0 150 4 28 0 0 0 0 2 60 5 29 35 45 150 36 600 1200 4 30 4 8 60 5 10 247 3 31 16 14 85 3 9 290 2 32 2 2 25 3 1 58 2 33 18 15 85 4 0 400 4 34 4 4 20 4 0 75 3 35 . . 200 0 0 . 5 36 6 3 0 0 0 144 4 37 2 2 0 1 0 65 4 38 . . 210 0 0 . 3 39 6 32 111 33 0 465 4 40 10 5 0 0 0 . 5 41 30 25 152 20 15 510 5 42 9 16 62 22 0 440 3 43 30 12 165 12 182 608 4 44 3 18 68 8 6 200 3 45 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