Notes: Singular Value Decomposition in Regression Analysis

Ivan Jacob Agaloos Pesigan

2020-12-31

Load Data

data(
  svd.linreg,
  package = "jeksterslabRdatarepo"
)

Data A

dataa <- as.data.frame(
  cbind(
    y = svd.linreg$ya,
    svd.linreg$Xa
  )
)

Data B

datab <- as.data.frame(
  cbind(
    y = svd.linreg$yb,
    svd.linreg$Xb
  )
)

Data Table

Data A

Data B

Plots

Scatter Plot Matrix

Data A

Data B

Descritive Statistics

Data A

	y	x1	x2	x3
	Min. :31.01	Min. :1	Min. :12.63	Min. :-4.6100
	1st Qu.:38.50	1st Qu.:1	1st Qu.:16.12	1st Qu.:-0.4975
	Median :40.27	Median :1	Median :17.82	Median : 0.6900
	Mean :41.06	Mean :1	Mean :18.15	Mean : 0.6050
	3rd Qu.:44.89	3rd Qu.:1	3rd Qu.:19.48	3rd Qu.: 2.0425
	Max. :50.05	Max. :1	Max. :24.81	Max. : 4.9300

	vars	n	mean	sd	median	trimmed	mad	min	max	range	skew	kurtosis	se
y	1	8	41.06125	5.868732	40.275	41.06125	5.233578	31.01	50.05	19.04	-0.1141907	-1.1296998	2.074910
x1	2	8	1.00000	0.000000	1.000	1.00000	0.000000	1.00	1.00	0.00	NaN	NaN	0.000000
x2	3	8	18.14750	3.739044	17.815	18.14750	2.779875	12.63	24.81	12.18	0.3269671	-1.0400238	1.321952
x3	4	8	0.60500	2.891707	0.690	0.60500	2.290617	-4.61	4.93	9.54	-0.2787964	-0.9637147	1.022373

Data B

	y	x1	x2	x3
	Min. :31.01	Min. :1	Min. :12.63	Min. :-3.6075
	1st Qu.:38.50	1st Qu.:1	1st Qu.:16.12	1st Qu.: 0.3881
	Median :40.27	Median :1	Median :17.82	Median : 1.6387
	Mean :41.06	Mean :1	Mean :18.15	Mean : 1.3894
	3rd Qu.:44.89	3rd Qu.:1	3rd Qu.:19.48	3rd Qu.: 2.9100
	Max. :50.05	Max. :1	Max. :24.81	Max. : 5.5275

	vars	n	mean	sd	median	trimmed	mad	min	max	range	skew	kurtosis	se
y	1	8	41.061250	5.868732	40.27500	41.061250	5.233578	31.0100	50.0500	19.040	-0.1141907	-1.129700	2.0749100
x1	2	8	1.000000	0.000000	1.00000	1.000000	0.000000	1.0000	1.0000	0.000	NaN	NaN	0.0000000
x2	3	8	18.147500	3.739044	17.81500	18.147500	2.779875	12.6300	24.8100	12.180	0.3269671	-1.040024	1.3219517
x3	4	8	1.389375	2.804283	1.63875	1.389375	2.084906	-3.6075	5.5275	9.135	-0.3269671	-1.040024	0.9914638