quiz 16

In a study to identify factors that influence territory sales and to assess the relative importance of the factors, four predictor variables were chosen, as defined below. Data from a random sample of 25 sales territories of a firm's national sales organization were analyzed. The first order linear model is:

The purpose of this exercise is to build a multiple regression model to predict y.

Y = sales credited to territory salesman

X1= length of time employed by company, in months

X2= industry sales, in units, of products sold in territory.

X3= advertising dollars in territory

X4= weighted average of past market share magnitudes for 4 previous years

X5= change over four years previous to time period analyzed

X6= total number of accounts assigned to a salesman

X7= Average workload per account

X8= performance rating by a supervisor on a scale of 1-7

The data is presented in an excel file.

We will use the stepwise option in PC SAS to get our model to use. The SAS output is presented in a separate file.

The questions you will be asked in the quiz link are as follows:

Q1:Which variables were found to be significant by conducting Stepwise Regression?

You must input them in the order in which they appear in the output and you may use commas and spaces between each variable.

Q2:now write the model that should be used in predicting y. use the same order as in Q1.

Q3:Now write the resulting prediction equation. Use the same order as in Q2.

JMP

Stepwise Fit for Y

Stepwise Regression Control

Stopping Rule:

P-value Threshold

Prob to Enter	0.25
Prob to Leave	0.1

Direction:

Forward

SSE	DFE	RMSE	RSquare	RSquare Adj	Cp	p	AICc	BIC
3213515.9	19	411.25712	0.9224	0.9019	3.798834	6	385.6352	387.5791

Current Estimates

Lock	Entered	Parameter	Estimate	nDF	SS	"F Ratio"	"Prob>F"
[x]	[x]	Intercept	-1280.1757	1	0	0.000	1
[]	[]	X1	0	1	188.4419	0.001	0.97444
[]	[x]	X2	0.0359169	1	4981711	29.455	0.00003
[]	[x]	X3	0.16523641	1	3741185	22.120	0.00015
[]	[x]	X4	194.853972	1	3228116	19.086	0.00033
[]	[x]	X5	330.205575	1	785009	4.641	0.04425
[]	[x]	X6	8.06750365	1	1570542	9.286	0.00663
[]	[]	X7	0	1	126984	0.741	0.4008
[]	[]	X8	0	1	24534.84	0.138	0.71414

Step History

Step		Parameter	Action	"Sig Prob"	Seq SS	RSquare	Cp	p	AICc	BIC
1		X6	Entered	0.0000	23597866	0.5702	71.993	2	414.97	417.484	()
2		X3	Entered	0.0002	8486365	0.7752	29.631	3	401.62	404.496	()
3		X2	Entered	0.0126	2432224	0.8340	18.916	4	397.202	400.138	()
4		X4	Entered	0.0011	2871982	0.9034	5.9025	5	387.178	389.824	()
5		X5	Entered	0.0443	785009	0.9224	3.7988	6	385.635	387.579	(x)

sales data

y	x1	x2	x3	x4	x5	x6	x7	x8
3670	43.1	74065	4583	2.51	0.34	75	15.05	4.9
3474	108.1	58117	5540	5.51	0.15	107	19.97	5.1
2295	13.8	21119	2950	10.91	-0.72	97	17.34	2.9
4676	186.2	68521	2243	8.27	0.17	195	13.4	3.4
6126	161.8	57805	7747	9.15	0.5	180	17.64	4.6
5032	365	50935	3141	8.54	0.55	256	18.8	4.6
3368	220.3	65602	2086	7.07	-0.49	127	19.86	2.3
6520	127.6	46177	8846	12.54	1.24	203	17.42	4.9
4876	105.7	42053	5673	8.85	0.31	120	21.41	2.8
2468	57.7	36830	2762	5.38	0.37	116	16.32	3.1
2533	23.6	33613	1992	5.43	-0.65	142	14.51	4.2
2408	13.8	21413	1972	8.48	0.64	89	19.35	4.3
2337	13.8	20417	1737	7.8	1.01	85	20.02	4.2
4587	87	36272	10694	10.34	0.11	120	15.26	5.5
2729	165.9	23093	8619	5.15	0.04	81	15.87	3.6
3289	116.3	26879	7748	6.64	0.68	137	7.81	3.4
2801	42.3	39572	4566	5.45	0.66	79	16	4.2
3264	52.8	51866	6023	6.31	-0.1	137	17.44	3.6
3454	165	58750	3721	6.35	-0.03	138	17.98	3.1
1741	10.6	23991	861	7.37	-1.63	76	20.99	1.6
2036	13.8	25695	3572	8.39	-0.43	102	21.66	3.4
1578	8.1	23736	2846	5.15	0.04	76	21.46	2.7
4167	58.5	34314	5060	12.88	0.22	137	24.78	2.8
2800	21.1	22810	3552	9.14	-0.74	89	24.96	3.9
2135	8.9	37807	402	5.51	0.15	105	16.22	4.5