Evaluate the polynomial $\mathit{p}（（\mathit{X}）=3{\mathit{X}}^2+2\mathit{X}+1$at the points $\mathit{X}=5，，，，7，，，，9$。多项式系数可以由矢量表示[[321]。

p = [3 2 1];x = [5 7 9];y = polyval（p，x）

y=1×386 162 262

评估确定的积分

Create a vector to represent the polynomial integrand $$3X^4-4X^2+10X-25$$。的 ${\mathit{X}}^3$term is absent and thus has a coefficient of 0.

p=[[30-410-25];

利用polyintto integrate the polynomial using a constant of integration equal to0。

Q =polyint（（p）

Q =1×60。6000 0 -1.3333 5.0000 -25.0000 0

Find the value of the integral by evaluating问在整合的范围内。

a = -1;b = 3;i = diff（polyval（q，[a b]））

i = 49.0667

Fit a linear model to a set of data points and plot the results, including an estimate of a 95% prediction interval.

Create a few vectors of sample data points（（X，，，，y）。利用polyfit为了将第一度多项式拟合到数据。指定两个输出以返回线性拟合以及误差估计结构的系数。

x = 1：100;y = -0.3*x + 2*randn（1,100）;[p，s] = polyFit（x，y，1）;

评估一级多项式拟合p在X。将误差估计结构指定为第三个输入，以便polyval计算估计的标准误差。的standard error estimate is returned in三角洲。

[y_fit，delta] = polyval（p，x，s）;

Plot the original data, linear fit, and 95% prediction interval $\mathit{y}\pm 2\Delta$。

情节（x，y，'bo'） 抓住上情节（x，y_fit，'r-'）plot(x,y_fit+2*delta,'M--'，x，y_fit-2*delta，'M--'）title('Linear Fit of Data with 95% Prediction Interval'）legend('Data'，，，，“线性拟合”，，，，'95％的预测间隔'）

Create a table of population data for the years 1750 - 2000 and plot the data points.

年=（（1750:25:2000)'; pop = 1e6*[791 856 978 1050 1262 1544 1650 2532 6122 8170 11560]'; T = table(year, pop)

T=11×2桌年pop ____ _________ 1750 7.91e+08 1775 8.56e+08 1800 9.78e+08 1825 1.05e+09 1850 1.262e+09 1875 1.544e+09 1900 1.65e+09 1925 2.532e+09 1950 6.122e+09 1975 8.17e+09 2000 1.156e+10

plot(year,pop,'o'）

利用polyfitwith three outputs to fit a 5th-degree polynomial using centering and scaling, which improves the numerical properties of the problem.polyfit中心数据年at 0 and scales it to have a standard deviation of 1, which avoids an ill-conditioned Vandermonde matrix in the fit calculation.

[p，〜，mu] = polyFit（t.year，t.pop，5）;

利用polyval有四个输入来评估p随着时间的扩展，（Year-mu（1））/MU（2）。将结果与原始年份相对。

f = polyVal（p，Year，[]，Mu）;抓住上情节（年，f）持有离开