统计计算与R填空题试题库及答案.docx

1、统计计算与R填空题试题库及答案第二章 R软件的使用1.求解非线性方程组一般用Newton法。Newton法的迭代格式为：其中J(x)为函数f(x)的Jacobi矩阵。请补全以下程序：Newtons = function (fun, x, ep=1e-5, it_max=100) index = 0; k = 1 while (k=it_max) x1 = x; obj = fun(x); x = x - _ (obj$J, obj$f); norm = sqrt(x-x1) %*% (x-x1) if (normep) index = 1; _ k = k+1 obj = fun(x); li

2、st(root=_, it=_, index=index, FunVal= _)funs = function(x) f = c(x12+x22-5, (x1+1)*x2-(3*x1+1)J = matrix(c(2*x1, 2*x2, x2-3, x1+1), nrow=2, byrow=T) list(f=f, J=J)2.编写一个R程序函数.输入一个整数n，如果，那么中止运算，并输出一句话:要求输入一个正整数; 否那么，如果n是偶数，那么将n除以2，并赋给n;否那么，将3 n + 1赋给n.不断循环，只到n = 1，才停顿计算，并输出一句话:运算成功.这个例子是为了检验数论中的一个简单的

3、定理. 请补全以下程序：fn = function(n) if(n0) _ else if (P x = c(0.10, 0.11, 0.12, 0.13, 0.14, 0.15,0.16, 0.17, 0.18, 0.20, 0.21, 0.23) y = c(42.0, 43.5, 45.0, 45.5, 45.0, 47.5,49.0, 53.0, 50.0, 55.0, 55.0, 60.0) lm.sol = lm(y 1+x) summary(lm.sol)Call:lm(formula = y 1 + x)Residuals:Min 1Q Median 3Q Max-2.0431

4、 -0.7056 0.1694 0.6633 2.2653Coefficients:Estimate Std. Error t value Pr(|t|)(Intercept) _ _ _5.88e-09 *x 130.835 9.683 13.51 9.50e-08 *-Signif. codes: 0 * 0.001 * 0.01 * 0.05 . 0.1 1Residual standard error: _ on 10 degrees of freedomMultiple R-Squared: _, Adjusted R-squared: 0.9429F-statistic: 182.

5、6 on 1 and 10 DF, p-value: 9.505e-08第七章方差分析14请补全单因素方差分析表。因素A r-1 MSA=_ F=_ p误差 n-r MSE=_总和 _ _第八章应用多元分析(I)1.请补全以下程序。discriminiant.distance = function (TrnX1, TrnX2, _ = NULL, var.equal = FALSE) if (is.null(TstX) = TRUE) TstX = rbind(TrnX1,TrnX2) if (is.vector(TstX) = TRUE) TstX = _ else if (is.matri

6、x(TstX) != TRUE) TstX = as.matrix(TstX) if (is.matrix(TrnX1) != TRUE) TrnX1 = as.matrix(TrnX1) if (is.matrix(TrnX2) != TRUE) TrnX2 = as.matrix(TrnX2) nx = nrow(TstX) blong = matrix(rep(0, nx), nrow=1, byrow=TRUE, dimnames=list(blong, 1:nx) mu1 = colMeans(TrnX1); mu2 = colMeans(TrnX2) if (_) S = _ (r

7、bind(TrnX1,TrnX2) w = mahalanobis(TstX, mu2, S)-mahalanobis(TstX, mu1, S) else S1 = var(TrnX1); S2 = var(TrnX2) w = mahalanobis(TstX, mu2, S2)-mahalanobis(TstX, mu1, S1) for (i in 1:nx) if (wi0) blongi = 1 else blongi = 2 _2.请补全以下程序。distinguish.distance = function (TrnX, _, TstX = NULL, var.equal =

8、FALSE) if (_ = FALSE) mx = nrow(TrnX); mg = nrow(TrnG) TrnX = rbind(TrnX, TrnG) TrnG = factor(rep(1:2, c(mx, mg) if (is.null(TstX) = TRUE) TstX = TrnX if (is.vector(TstX) = TRUE) TstX = t(as.matrix(TstX) else if (is.matrix(TstX) != TRUE) TstX = as.matrix(TstX) if (is.matrix(TrnX) != TRUE) TrnX = as.

9、matrix(TrnX) nx = nrow(TstX) blong = matrix(rep(0, nx), nrow=1, dimnames=list(blong, 1:nx) g = length(levels(TrnG) mu = matrix(0, nrow=g, ncol=ncol(TrnX) for (i in 1:g) mui, = colMeans(TrnXTrnG=i,) D = matrix(0, nrow=g, ncol=nx)if (_) for (i in 1:g) Di, = _ else for (i in 1:g) Di, = mahalanobis(TstX

10、, mui, var(TrnXTrnG=i,) for (j in 1:nx)_ for (i in 1:g) if (Di,jdmin) dmin = Di,j; blongj = i blong3.请补全以下程序。discriminiant.bayes = function (TrnX1, TrnX2, _, TstX = NULL, var.equal = FALSE) if (is.null(TstX) = TRUE) TstX = rbind(TrnX1,TrnX2) if (is.vector(TstX) = TRUE) TstX = t(as.matrix(TstX) else

11、if (is.matrix(TstX) != TRUE) TstX = as.matrix(TstX) if (is.matrix(TrnX1) != TRUE) TrnX1 = as.matrix(TrnX1) if (is.matrix(TrnX2) != TRUE) TrnX2 = as.matrix(TrnX2) nx = nrow(TstX) blong = matrix(rep(0, nx), nrow=1, byrow=TRUE, dimnames=list(blong, 1:nx) mu1 = colMeans(TrnX1); mu2 = colMeans(TrnX2) if

12、(_) S = var(rbind(TrnX1,TrnX2); beta = _ w = _ else S1 = var(TrnX1); S2 = var(TrnX2) beta = 2*log(rate)+log(det(S1)/det(S2) w = mahalanobis(TstX, mu2, S2)-mahalanobis(TstX, mu1, S1) for (i in 1:nx) if (_) blongi = 1 else blongi = 2 blong第九章应用多元分析(II)4.下面是主成分法的R程序，请补全它。factor.analy1 = function(S, m)

13、p = nrow(S); diag_S = diag(S); sum_rank = sum(diag_S) rowname = paste(X, 1:p, sep=) colname = paste(Factor, 1:m, sep=) A = matrix(0, nrow=p, ncol=m, dimnames=list(rowname, colname) eig = _ for (i in 1:m) A,i = _*eig$vectors,i h = diag(_) rowname = c(SS loadings, Proportion Var, Cumulative Var)B = ma

14、trix(0, nrow=3, ncol=m, dimnames=list(rowname, colname) for (i in 1:m) B1,i = _ B2,i = B1,i/sum_rank B3,i = sum(B1,1:i)/sum_rank method = c(Principal ponent Method) list(method=method, loadings=A, var=_(mon=h, spcific=diag_S-h), B=B) 5.下面是主因子法的R程序，请补全它。factor.analy2 = function(_) p = nrow(R); diag_R

15、 = diag(R); sum_rank = sum(diag_R) rowname = paste(X, 1:p, sep=) colname = paste(Factor, 1:m, sep=) A = matrix(0, nrow=p, ncol=m, dimnames=list(rowname, colname) kmax=20; k = 1; h = _ diag(R) = h; h1 = h; eig = eigen(R) for (i in 1:m) A,i = sqrt(eig$valuesi)*eig$vectors,i h = diag(A %*% t(A) if (_0.

16、70) m = i; break _ (method, prinp=factor.analy1(S, m), factor=factor.analy2(S, m, d), likelihood=factor.analy3(S, m, d) ) 程序填空题题库答案第二章 R软件的使用1.求解非线性方程组一般用Newton法。Newton法的迭代格式为：其中J(x)为函数f(x)的Jacobi矩阵。请补全以下程序：Newtons = function (fun, x, ep=1e-5, it_max=100) index = 0; k = 1 while (k=it_max) x1 = x; obj = fun(x); x = x - solve(obj$J, obj$f); norm = sqrt(x-x1) %*% (x-x1) if (norm