统计学教材部分参考答案(第三版)

(3)72000=1085.76x(1+13.55%)=1232.88。10.2下表是1981年—2000年我国油彩油菜籽单位面积产量数据(单位：kg/hm2)年份单位面积产量年份单位面积产量1981145119911215198213721992128119831168199313091984123219941296198512451995141619861200199613671987126019971479198810201998127219891095199914691990126020001519(1)绘制时间序列图描述其形态。(2)用5期移动平均法预测2001年的单位面积产量。分析预测(3)采用指数平滑法，分别用平滑系数a=0.3和a=0.5预测2001年的单位面积产量,误差，说明用哪一个平滑系数预测更合适？分析预测详细答案：(1)时间序列图如下：（2）2001年的预测值为：（2）2001年的预测值为：1367+1479+1272+1469+15197106年份单位面积产量指数平滑预测|a—0.3误差平方指数平滑预测a=0.5误差平方19811451198213721451.06241.01451.06241.0198311681427.367236.51411.559292.3(3)由Excel输出的指数平滑预测值如下表:198412321349.513808.61289.83335.1|198512451314.34796.51260.9252.01986120011293.58738.51252.92802.4198712601265.429.5|1226.51124.3198810201263.859441.01243.249833.6198910951190.79151.51131.61340.8199012601162.09611.01113.321518.4|199112151191.4558.11186.7803.5199212811198.56812.41200.86427.7199313091223.2|7357.611240.94635.8|199412961249.02213.11275.0442.81199514161263.123387.71285.517035.9199613671308.93369.91350.7264.4|199714791326.423297.71358.914431.3199812721372.210031.01418.921589.8199914691342.116101.51345.515260.3200015191380.219272.11407.212491.7合计■，,291455.2239123.02001年a=0.3时的预测值为：=叱+(1-司月=Q.3xl519+(l-Q3Jxm=B211a二0.5时的预测值为：%产苗+。-4)月=05x1519+(1-0.5)x14071=14Hl比较误差平方可知，a=0.5更合适。10.3下面是一家旅馆过去18个月的营业额数据月份营业额（万元）月份营业额（万元）129510473228311470332212481435513449528614544637915|601738116587843117644

9424I18|€)60(1)用3期移动平均法预测第19个月的营业额。(2)采用指数平滑法，分别用平滑系数a=0.3、a=0.4和a=0.5预测各月的营业额，分析预测误差，说明用哪一个平滑系数预测更合适？(3)建立一个趋势方程预测各月的营业额，计算出估计标准误差。详细答案：(1)第19个月的3期移动平均预测值为：5.+也660二空「630333(2)月份营业额预测3.—0.3误差平方预测a=0.4误差平方预测1a=0.5误差平方12952283295.0[44.0295.0144.0295.01M.03322291,4[936.4290.21011.2289.01089.0■4355300.62961.5302.92712.3305.52450.35286316.9955.2323.81425.2330.31958.16■379307.65093.1308.74949.0308.15023.317381329.02699.4336.81954.5343.61401.68431344.67459.6354.55856.2362.34722.39424370.52857.8385.11514.4396.6748.510473386.67468.6400.75234.4410.33928.711•470412.53305.6429.61632.9441.7803.1124811429.82626.2445.81242.3455.8633.513449445.1|15.0459.9117.8468.4376.914544|446.39547.4455.57830.2458.77274.815|601口475.615724.5490.912120.5501.49929.416587513.25443.2534.92709.8551.21283.317644535.411803.7555.87785.2569.15611.718660567.98473.4591.14752.7606.52857.5合计——87514.7——62992.550236由Excel输出的指数平滑预测值如下表：a=0.3时的预测值:4=0,3x660+(17.3)x5679=595,5,误差均方二87514.7oa=0.4时的预测值：均=0取660+(1-065外1=邹7,误差均方二629925。

a=0.5时的预测值:&g=05x660+(!-05)x606.5=633,误差均方=50236比较各误差平方可知，a=0.5更合适。（3）根据最小二乘法，利用Excel输出的回归结果如下:回归统计MultpleR0.9673RSquare0.9356AdjjstedRSquarc0.9316标准误差31.6628观测值18方差分析dfSSMSF|S垣niScanceF回归分析1232982.5232982.5232.39445.99E-11残差1616040.491002.53总计17249022.9Coefficients标准误差tStatP^vaheLower95%Upper95%Jhtercept239.7