Question

For the attached data set, create a multiple linear regression equation with profit as the dependent variable and R&D spend, Administration expenses and Marketing spend as the independent variables.

Please answer these 3 questions below.

1. Comment on the adequacy of the model.

2. Identify the predictors that are significant.

3. Interpret the coefficient of determination.

R&D Spend($)	Administration ($)	Marketing Spend ($)	Profit ($)
165349	136898	471784	192262
162598	151378	443899	191792
153442	101146	407935	191050
144372	118672	383200	182902
142107	91392	366168	166188
131877	99815	362861	156991
118672	147199	127717	156123
130298	145530	323877	155753
120543	148719	311613	152212
123335	108679	304982	149760
101913	110594	229161	146122
100672	91791	249745	144259
93864	127320	249839	141586
91992	135495	252665	134307
119943	156547	256513	132603
114524	122617	261776	129917
78013	121598	264346	126993
94657	145078	282574	125370
91749	114176	294920	124267
76254	113867	298664	118474
78389	153773	299737	111313
73995	122783	303319	110352
67533	105751	304769	108734
77044	99281	140575	108552
64665	139553	137963	107404
75329	144136	134050	105734
72108	127865	353184	105008
66052	182646	118148	103282
65605	153032	107138	101005

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.96507787	0.96507787
R Square	0.93137529	0.93137529
Adjusted R Square	0.92314032
Standard Error	7895.11433
Observations	29
ANOVA
	df	SS	MS	F	Significance F
Regression	3	21149545193	7049848398	113.1001	1.13593E-14
Residual	25	1558320756	62332830.24
Total	28	22707865949
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	57559.3856	11367.44409	5.063529246	3.16E-05	34147.69626	80971.07	34147.7	80971.07
R&D Spend($)	0.81119127	0.06324241	12.82669766	1.7E-12	0.680941092	0.941441	0.680941	0.941441
Administration ($)	-0.083838	0.069633656	-1.203986514	0.239871	-0.227251182	0.059575	-0.22725	0.059575
Marketing Spend ($)	0.02222515	0.021498499	1.03380026	0.311127	-0.022051834	0.066502	-0.02205	0.066502

RESIDUAL OUTPUT
Observation	Predicted Profit ($)	Residuals
1	190697.453	1564.377223
2	186631.743	5160.317491
3	182616.369	8434.021238
4	173240.487	9661.50307
5	173311.668	-7123.727744
6	164233.162	-7242.041868
7	157255.942	-1133.4318
8	158253.354	-2500.754169
9	149799.783	2411.987375
10	155274.385	-5514.425192
11	136051.537	10070.41283
12	137078.673	7180.72735
13	128579.277	13006.2432
14	126438.693	7868.656669
15	147432.715	-14830.06457
16	145998.007	-16080.96726
17	116523.578	10469.35166
18	128461.694	-3091.323775
19	128967.869	-4700.968596
20	116507.311	1966.719394
21	114917.893	-3604.872951
22	114030.586	-3678.336242
23	110248.764	-1514.773636
24	114857.564	-6305.523791
25	101381.219	6023.120827
26	109560.721	-3827.181299
27	113182.1	-8173.790205
28	98453.0289	4829.351087
29	100329.246	675.3936851

Answer 1

1. Comment on the adequacy of the model: From the output we can see that R Square / Adjusted R Square value is very high (0.93/0.92). Where as the range of R Square is in between 0 -1. Large R Square does not measure the appropriateness of the linear model. It does not imply that the regression model will predict accurately. Here residual values are very high as well.

2. Identify the predictors that are significant : Only R&D Spend($) variable is significant at 5% confidence level as P value is

1.7E-12 (<0.05).

3. Interpret the coefficient of determination : coefficient of determination is the ratio between explained variation and total variation. It tells us how much variability can be explained by the model.

PLEASE LET ME KNOW IF YOU HAVE ANY DOUBTS. THANKS!