统计计算 与R 填空题题库及答案.doc

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。请补全下列程序：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); list(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，则中止运算，并输出一句话:“要求输入一个正整数”; 否则，如果n是偶数，则将n除以2，并赋给n;否则，将3 n + 1赋给n.不断循环，只到n = 1，才停止计算，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定理. 请补全下列程序：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 -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: 182.6 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.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 (_) S = _ (rbind(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 = 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.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, 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 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 (_) 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) 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$vectors,i h = diag(_) rowname = c(SS loadings, Proportion Var, Cumulative Var) B = matrix(0, nrow=3, ncol=m, dimnames=list(rowname, colname) for (i in 1:m) B1,i = _ B2,i = B1,i/sum_rank B3,i = sum(B1,1:i)/sum_rank method = c(Principal Component Method) list(method=method, loadings=A, var=_(common=h, spcific=diag_S-h), B=B) 5. 下面是主因子法的R程序，请补全它。factor.analy2 = function(_) p = nrow(R); diag_R = diag(R); sum_rank = sum(diag_R) rowname = paste(X, 1:p, sep=) colname = paste(Factor, 1:m, sep=) A = matrix(0, nrow=p, ncol=m, dimnames=list(rowname, colname) kmax=20; k = 1; h = _ _ diag(R) = h; h1 = h; eig = eigen(R) for (i in 1:m) A,i = sqrt(eig$valuesi)*eig$vectors,i h = diag(A %*% t(A) if (_0.70) m = i; break source(factor.analy1.R) source(factor.analy2.R) source(factor.analy3.R) _ (method, princomp=factor.analy1(S, m), factor=factor.analy2(S, m, d), likelihood=factor.analy3(S, m, d) ) 程序填空题题库答案第二章 R软件的使用1. 求解非线性方程组一般用Newton法。Newton法的迭代格式为：其中J(x)为函数f(x)的Jacobi矩阵。请补全下列程序：Newtons = function (fun, x, ep=1e-5, it_max=100) index = 0; k = 1 while (k=it_max) x1 = x; obj = fun(x); x = x - solve(obj$J, obj$f); norm = sqrt(x-x1) %*% (x-x1) if (normep) index = 1; break k = k+1 obj = fun(x); list(root=x, it=k, index=index, FunVal= obj$f)2. 编写一个R程序（函数）.输入一个整数n，如果，则中止运算，并输出一句话:“要求输入一个正整数”; 否则，如果n是偶数，则将n除以2，并赋给n;否则，将3 n + 1赋给n.不断循环，只到n = 1，才停止计算，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定理. 请补全下列程序：fn = function(n) if(n0) n = (3*n+1) if(n=1) breaki=i+1 list(result=运算成功, n=n, iter=i) 第三章 数据描述性分析3. data_outline.R计算样本的各种描述性统计量。请补全该程序。data_outline = function(x) n = length(x) m = mean(x) v = var(x) s = sd(x) me = median(x) cv = 100*s/m css = sum(x-m)2) uss = sum(x2) R = max(x)-min(x) R1 = quantile(x,3/4)-quantile(x,1/4) sm = s/sqrt(n) g1 = n/(n-1)*(n-2)*sum(x-m)3)/s3 g2 = (n*(n+1)/(n-1)*(n-2)*(n-3)*sum(x-m)4)/s4 - (3*(n-1)2)/(n-2)*(n-3) data.frame(N=n, Mean=m, Var=v, std_dev=s, Median=me, std_mean=sm, CV=cv, CSS=css, USS=uss, R=R, R1=R1, Skewness=g1, Kurtosis=g2, s=1)第四章 参数估计4. 请写出正态均值、方差区间估计及假设检验，非正态均值区间估计的函数名（共23个程序）正态均值区间估计及假设检验单总两总Sigma已知Sigma未知Sigma1, sigma2已知Sigma1, sigma2未知=Sigma1, sigma2未知!=区间估计interval_estimate1(双)interval_estimate2(双)interval_estimate4(单、双)interval_estimate5(单、双)t.test(单、双)Xt.test(单、双、成对)X假设检验mean.test1mean.test2interval_estimate4(区)interval_estimate5(区)t.test(区)Xt.test(区、成对)X正态方差区间估计及假设检验单总两总Mu已知Mu未知mu1, mu2已知mu1, mu2未知区间估计interval_var1(双)interval_var2(双)interval_var3(单、双)interval_var4 (单、双)var.test(单、双)X假设检验var.test1var.test2interval_var3(区)interval_var4(区)var.test(区)X非正态均值区间估计：interval_estimate3(双)5. 单个正态总体均值的区间估计函数是interval_estimate1.R, 请补全此程序。interval_estimate1 = function(x, sigma=-1, alpha=0.05) n = length(x); xb = mean(x) if (sigma=0) tmp = sigma/sqrt(n)*qnorm(1-alpha/2); df = n else tmp = sd(x)/sqrt(n)*qt(1-alpha/2,n-1); df = n-1 data.frame(mean=xb, df=df, a=xb-tmp, b=xb+tmp)6. 单个正态总体方差的区间估计函数是interval_var1.R, 请补全此程序。interval_var1 = function(x, mu=Inf, alpha=0.05) n = length(x) if (muInf) S2 = sum(x-mu)2)/n; df = n else S2 = var(x); df = n-1 a = df*S2/qchisq(1-alpha/2,df) b = df*S2/qchisq(alpha/2,df) data.frame(var=S2, df=df, a=a, b=b)第五章 假设检验7. P_value.R为求P值的R程序，请补全它。P_value = function(cdf, x, paramet=numeric(0), side=0) n = length(paramet) P = switch(n+1, cdf(x), cdf(x, paramet), cdf(x, paramet1, paramet2), cdf(x, paramet1, paramet2, paramet3) ) if (side0) 1-P else if (P=0) z = (xb-mu)/(sigma/sqrt(n) P = P_value(pnorm, z, side=side) data.frame(mean=xb, df=n, Z=z, P_value=P) else t = (xb-mu)/(sd(x)/sqrt(n) P = P_value(pt, t, paramet=n-1, side=side) data.frame(mean=xb, df=n-1, T=t, P_value=P) 9. var.test1.R是求单个正态总体方差检验的R程序，请补全它。var.test1 = function(x, sigma2=1, mu=Inf, side=0) source(P_value.R) n = length(x) if (mu 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 -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: 182.6 on 1 and 10 DF, p-value: 9.505e-08第七章 方差分析11. 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 n-1 第八章 应用多元分析(I)12. 请补全以下程序。discriminiant.distance = 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 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 (var.equal = = TRUE) S = var(rbind(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 blong13. 请补全以下程序。distinguish.distance = function (TrnX, TrnG, TstX = NULL, var.equal = FALSE) if ( is.factor(TrnG) = 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(Tst