Question

College Graduation and Other State Characteristics (n = 50, k = 8)
										omit
State	ColGrad%	Dropout	EdSpend	Metro%	Age	LPRFem	Neast	Seast	West	Midwest
AL	19.8	19.1	1221	89.2	37.4	55.8	0	1	0	0
AK	28.7	8.3	2187	74.7	33.9	65.6	0	0	1	0
AZ	27.9	14.3	1137	96.7	34.5	57.4	0	0	1	0
AR	17.5	18.6	1158	78.8	37.0	54.9	0	1	0	0
CA	30.4	19.7	1657	99.3	34.4	57.6	0	0	1	0
CO	35.4	10.8	1599	91.6	34.7	65.3	0	0	1	0
CT	36.9	10.0	2142	100.0	39.3	60.0	1	0	0	0
DE	25.6	13.2	1687	100.0	37.9	61.1	1	0	0	0
FL	25.5	13.2	1286	97.8	39.5	55.4	0	1	0	0
GA	26.9	14.3	1648	91.0	34.3	59.2	0	1	0	0
HI	30.6	12.7	1347	100.0	38.5	60.1	0	0	1	0
ID	25.9	10.9	1244	86.1	34.6	61.3	0	0	1	0
IL	29.5	12.7	2334	95.2	35.6	59.7	0	0	0	1
IN	22.5	12.8	1644	94.1	36.1	61.0	0	0	0	1
IA	24.5	10.1	1407	72.4	38.6	65.4	0	0	0	1
KS	30.4	8.6	1418	84.7	36.1	64.5	0	0	0	1
KY	19.0	21.1	1263	75.6	37.5	55.4	0	1	0	0
LA	19.7	19.8	1367	93.2	35.4	54.9	0	1	0	0
ME	24.2	12.8	1716	70.5	41.2	61.0	1	0	0	0
MD	36.3	13.0	1627	98.5	37.1	62.3	1	0	0	0
MA	36.8	12.5	1807	99.6	38.2	61.9	1	0	0	0
MI	24.6	11.5	1880	92.1	36.9	59.7	0	0	0	1
MN	34.3	7.3	1860	87.2	36.7	69.0	0	0	0	1
MS	21.9	20.1	1178	77.8	35.5	55.5	0	1	0	0
MO	24.9	14.6	1288	86.2	37.4	62.7	0	0	0	1
MT	25.4	7.9	1312	64.8	40.2	62.0	0	0	1	0
NE	25.1	10.3	1373	79.7	36.2	68.5	0	0	0	1
NV	23.5	13.4	1516	98.0	35.2	59.3	0	0	1	0
NH	32.8	8.1	1632	96.4	39.5	64.7	1	0	0	0
NJ	36.3	13.0	1903	100.0	38.0	58.4	1	0	0	0
NM	27.2	19.0	1608	95.9	36.2	57.5	0	0	1	0
NY	30.3	14.4	2046	97.7	37.5	56.2	1	0	0	0
NC	25.4	16.0	1233	91.7	36.2	58.8	0	1	0	0
ND	27.2	10.0	1316	69.2	39.1	67.6	0	0	0	1
OH	22.9	12.1	1667	95.5	37.6	60.4	0	0	0	1
OK	24.0	14.8	1163	84.2	36.5	57.6	0	0	0	1
OR	29.1	11.3	1384	96.1	37.0	59.0	0	0	1	0
PA	25.8	13.7	1617	96.9	39.7	58.1	1	0	0	0
RI	29.2	16.0	1594	100.0	38.4	61.7	1	0	0	0
SC	24.2	17.0	1422	93.5	37.1	59.5	0	1	0	0
SD	25.1	11.5	1329	71.3	37.0	69.4	0	0	0	1
TN	21.6	18.2	1079	89.5	37.3	57.4	0	1	0	0
TX	25.4	21.8	1696	93.8	33.2	58.2	0	0	1	0
UT	29.8	7.3	1319	94.8	28.5	62.7	0	0	1	0
VT	34.4	10.0	1948	73.7	40.7	65.8	1	0	0	0
VA	30.7	13.9	1631	89.1	37.2	60.8	0	1	0	0
WA	30.9	8.5	1561	96.4	36.7	61.2	0	0	1	0
WV	15.1	17.6	1538	75.0	40.7	49.1	0	1	0	0
WI	25.1	9.5	1792	85.9	37.9	66.6	0	0	0	1
WY	22.0	9.1	1896	71.5	39.1	65.3	0	0	1	0

Does the VIF on the LPR FEM coefficient indicate that mulitcollinearity is a problem?

Answer 1

The following problem is solved in minitab 2017.

Regression Analysis: ColGrad% versus Dropout, EdSpend, LPRFem, Metro%, Age, Neast, Seast, ...

The following terms cannot be estimated and were removed:
Midwest

Method

Categorical predictor coding (1, 0)

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Regression 8 885.45 110.682 11.53 0.000
Dropout 1 18.76 18.757 1.95 0.170
EdSpend 1 18.70 18.704 1.95 0.170
LPRFem 1 81.48 81.480 8.49 0.006
Metro% 1 125.89 125.890 13.11 0.001
Age 1 2.74 2.738 0.29 0.596
Neast 1 108.81 108.807 11.33 0.002
Seast 1 12.91 12.915 1.34 0.253
West 1 37.11 37.115 3.87 0.056
Error 41 393.70 9.603
Total 49 1279.16

Model Summary

S R-sq R-sq(adj) R-sq(pred)
3.09879 69.22% 63.22% 55.22%

Coefficients

Term Coef SE Coef T-Value P-Value VIF
Constant -21.8 21.9 -0.99 0.327
Dropout -0.258 0.185 -1.40 0.170 2.64
EdSpend 0.00252 0.00181 1.40 0.170 1.45
LPRFem 0.548 0.188 2.91 0.006 3.17
Metro% 0.2036 0.0562 3.62 0.001 1.68
Age -0.146 0.273 -0.53 0.596 1.89
Neast
1 5.26 1.56 3.37 0.002 2.18
Seast
1 2.00 1.73 1.16 0.253 2.83
West
1 2.64 1.34 1.97 0.056 1.89

Regression Equation

Neast Seast West
0 0 0 ColGrad% = -21.8 - 0.258 Dropout + 0.00252 EdSpend + 0.548 LPRFem
+ 0.2036 Metro% - 0.146 Age

0 0 1 ColGrad% = -19.1 - 0.258 Dropout + 0.00252 EdSpend + 0.548 LPRFem
+ 0.2036 Metro% - 0.146 Age

0 1 0 ColGrad% = -19.8 - 0.258 Dropout + 0.00252 EdSpend + 0.548 LPRFem
+ 0.2036 Metro% - 0.146 Age

0 1 1 ColGrad% = -17.1 - 0.258 Dropout + 0.00252 EdSpend + 0.548 LPRFem
+ 0.2036 Metro% - 0.146 Age

1 0 0 ColGrad% = -16.5 - 0.258 Dropout + 0.00252 EdSpend + 0.548 LPRFem
+ 0.2036 Metro% - 0.146 Age

1 0 1 ColGrad% = -13.9 - 0.258 Dropout + 0.00252 EdSpend + 0.548 LPRFem
+ 0.2036 Metro% - 0.146 Age

1 1 0 ColGrad% = -14.5 - 0.258 Dropout + 0.00252 EdSpend + 0.548 LPRFem
+ 0.2036 Metro% - 0.146 Age

1 1 1 ColGrad% = -11.9 - 0.258 Dropout + 0.00252 EdSpend + 0.548 LPRFem
+ 0.2036 Metro% - 0.146 Age

Fits and Diagnostics for Unusual Observations

Obs ColGrad% Fit Resid Std Resid
8 25.60 32.64 -7.04 -2.41 R
44 29.80 31.80 -2.00 -0.97 X
50 22.00 27.93 -5.93 -2.21 R

R Large residual
X Unusual X

The VIF of LPRFem is 3.17.

Here as the VIF<5, then it can be concluded that multicollinearity is not a problem as such.