Question

1.Is there evidence of multicollinearity? Perform Factor analysis by extracting four factors and name for those factors.

Problem needs to solved using R

ID	ProdQual	Ecom	TechSup	CompRes	Advertising	ProdLine	SalesFImage	ComPricing	WartyClaim	OrdBilling	DelSpeed	Satisfaction
1	8.5	3.9	2.5	5.9	4.8	4.9	6	6.8	4.7	5	3.7	8.2
2	8.2	2.7	5.1	7.2	3.4	7.9	3.1	5.3	5.5	3.9	4.9	5.7
3	9.2	3.4	5.6	5.6	5.4	7.4	5.8	4.5	6.2	5.4	4.5	8.9
4	6.4	3.3	7	3.7	4.7	4.7	4.5	8.8	7	4.3	3	4.8
5	9	3.4	5.2	4.6	2.2	6	4.5	6.8	6.1	4.5	3.5	7.1
6	6.5	2.8	3.1	4.1	4	4.3	3.7	8.5	5.1	3.6	3.3	4.7
7	6.9	3.7	5	2.6	2.1	2.3	5.4	8.9	4.8	2.1	2	5.7
8	6.2	3.3	3.9	4.8	4.6	3.6	5.1	6.9	5.4	4.3	3.7	6.3
9	5.8	3.6	5.1	6.7	3.7	5.9	5.8	9.3	5.9	4.4	4.6	7

Answer 1

>plot(data)

>cor(data)

	ProdQual	Ecom	TechSup	CompRes	Advertising	ProdLine	SalesFImage	ComPricing	WartyClaim	OrdBilling	DelSpeed	Satisfaction
ProdQual	1.000	0.070	-0.026	0.260	0.005	0.570	0.029	-0.798	0.002	0.440	0.271	0.639
Ecom	0.070	1.000	-0.091	-0.167	0.000	-0.361	0.911	0.229	-0.157	0.117	-0.308	0.561
TechSup	-0.026	-0.091	1.000	-0.137	-0.094	0.263	-0.107	0.036	0.841	-0.008	-0.002	-0.159
CompRes	0.260	-0.167	-0.137	1.000	0.295	0.791	-0.032	-0.489	0.026	0.581	0.952	0.447
Advertising	0.005	0.000	-0.094	0.295	1.000	0.231	0.273	-0.324	0.235	0.690	0.388	0.313
ProdLine	0.570	-0.361	0.263	0.791	0.231	1.000	-0.236	-0.676	0.408	0.626	0.867	0.415
SalesFImage	0.029	0.911	-0.107	-0.032	0.273	-0.236	1.000	0.089	-0.099	0.291	-0.089	0.694
ComPricing	-0.798	0.229	0.036	-0.489	-0.324	-0.676	0.089	1.000	-0.038	-0.542	-0.576	-0.573
WartyClaim	0.002	-0.157	0.841	0.026	0.235	0.408	-0.099	-0.038	1.000	0.421	0.209	-0.042
OrdBilling	0.440	0.117	-0.008	0.581	0.690	0.626	0.291	-0.542	0.421	1.000	0.659	0.674
DelSpeed	0.271	-0.308	-0.002	0.952	0.388	0.867	-0.089	-0.576	0.209	0.659	1.000	0.439
Satisfaction	0.639	0.561	-0.159	0.447	0.313	0.415	0.694	-0.573	-0.042	0.674	0.439	1.000

Lets take y = ProdQual, remaning are independent variables (x)         // not given in problem

Correlation of Advertising, WartyClaim, SalesFImage, TechSup, is very less with ProdQual

hence these factors are removed from model

> fit <- lm(data$ProdQual ~ data$Satisfaction + data$Ecom + data$CompRes + data$ProdLine + data$ComPricing + data$OrdBilling + data$DelSpeed)

> summary(fit)

Call:
lm(formula = data$ProdQual ~ data$Satisfaction + data$Ecom + data$CompRes + data$ProdLine + data$ComPricing + data$OrdBilling + data$DelSpeed)

Residuals:
        1         2         3         4         5         6         7         8         9
-0.071003 -0.001687 -0.118268 -0.061503 0.245459 -0.075776 -0.034283 0.101407 0.015653

---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.317 on 1 degrees of freedom
Multiple R-squared: 0.9927,   Adjusted R-squared: 0.9413
F-statistic: 19.34 on 7 and 1 DF, p-value: 0.1734