R语言主成分分析案例 附代码数据

R语言主成分分析案例
Question1
Q1.1:
> print(eigen_values)
[1] 2.4802416 0.9897652 0.3565632 0.1734301
Q1.2
> print(eigen_vectors)
[,1] [,2] [,3] [,4]
[1,] -0.5358995 0.4181809 -0.3412327 0.64922780
[2,] -0.5831836 0.1879856 -0.2681484 -0.74340748
[3,] -0.2781909 -0.8728062 -0.3780158 0.13387773
[4,] -0.5434321 -0.1673186 0.8177779 0.08902432
Q1.3
> print('variance for each eigen_values')
[1] "variance for each eigen_values"
> print(scores)
Comp.1 Comp.2 Comp.3 Comp.4
0.9655342206 0.027******* 0.0057995349 0.0008489079
Question2:
Q2.1:
See in code
Q2.2:
The result of ordinary linear regression:
> OLS
Call:
lm(formula = Apps ~ ., data = collegeTrainData)
Coefficients:
(Intercept) Private Accept Enroll Top10perc Top25perc F.Undergrad
-8.753e+02 -6.409e+02 1.345e+00 -2.841e-01 4.792e+01 -1.465e+01 1.980e-02
P.Undergrad Outstate Room.Board Books Personal PhD Terminal
-1.612e-03 -4.370e-02 2.831e-01 2.356e-01 8.284e-02 1.552e-01 -9.877e+00
S.F.Ratio perc.alumni Expend Grad.Rate
1.547e+01 -6.582e+00 6.118e-02 4.944e+00
And the result in terms of MSE and r-squared is;
> print(mse)
[1] 1454941
> print(rsqured)
[1] 0.9162122
Q2.3:
Use the lambda of seq(0, 1, 0.05) in r, which means from 0 to 1 by 0.05,
The result by ridge regression of cross validation is:
> print(mse)
[1] 1464329
> print(ridgeRsquared)
[1] 0.9156716
Which is slightly worse than the ordinary linear regression.
Q2.3:
Use the lambda of seq(0, 1, 0.05) in r, which means from 0 to 1 by 0.05,
The result by lasso regression of cross validation is:
> mse
[1] 1471047
> LassoRsquared
[1] 0.9152847
And I make the following table to compare the parameters by the three different models:
It can found that Lasso set the parameter of “Phd” to 0. Then it can be inferred that the adjusted r-square of Lasso regression is the best among the three models.
Question3:
Q3.1:
> h_1 = sd(F12)*(4/3/length(F12))^(1/5)
> h_1
[1] 0.3101212
Q3.2:
> min(F12)
[1] -2.995732
> max(F12)
[1] 7.930889
The min value of log_F12 is -2.99, the maximum value is 7.93. Therefore, I choose the sample from -3 to 8 by 0.05, the following is the plot of the estimated density.
Q3.3:
I choose 4 different bandwidth:
h_2 <- 0.1
h_3 <- 0.2
h_4 <- 0.5
h_5 <- 0.7
And the following plot can be get:
The middle one is the plot by question b.
And the numerical summary of the simulated density for the five different bandwidth
We can see that the larger bandwidth will cause a evener gentler distribution.。