5.某企业在制定某商品的广告策略时，收集了该商品在不同地区采用不同广告形式促销后的销售额数据，希望对广告形式和地区是否对商品销售额产生影响进行分析，a)以商品销售额为因变量，广告形式和地区为自变量，通过单因素方差分析方法分别对广告形式、地区对销售额的影响进行分析；b)试进一步分析，究竟哪种广告形式的作用较明显，哪种不明显，以及销售额和地区之间的关系等。

c)试分析广告形式、地区以及两者的交互作用是否对商品销售额产生影响。

（数据见练习2数据.xls—练习2.5，其中广告形式为：1. 报纸；2. 广播；3. 宣传品；4. 体验）答：(a)i以广告形式为自变量时，0:H广告形式对销售额没有差异1H：广告形式对销售额有差异α=0.05通过SPSS分析可以得到下面的结论F分布值为2.6693本题所计算的结果13.483>2.6693决策：拒绝H结论：有显著证据表明，广告形式对销售额有显著差异ii以地区为自变量时H:地区对销售额没有影响1H：地区对销售额有影响构造检验统计量将数据导入SPSS进行单因素相关性分析F 分布值为1.7044 因为F>P=1.704 决策：拒绝0H结论：有显著证据表明，地区对销售额有影响 b) （i ）下面计算广告形式的影响 主要通过LSD 来比较使用matlab 计算t 分布值为： >> tinv(0.025,140)ans =-1.97715.61LSD === 现在构造假设检验量：i j x x -提出假设：0H :第i 中广告形式的和第j 种广告形式对销量没有显著性差异1H ：第i 中广告形式的和第j 种广告形式对销量有显著性差异结论：第1种广告形式和第2种广告形式的销量没有显著差异 第1种广告形式和第3种广告形式的销量有显著差异 第1种广告形式和第4种广告形式的销量有显著差异 第2种广告形式和第3种广告形式的销量有显著差异 第2种广告形式和第4种广告形式的销量没有显著差异 第3种广告形式和第4种广告形式的销量有显著差异 而且从均值图分析可以看出来，第1种广告形式对增加销量影响显著，第3种对于减少销量影响显著。

（ii ）下面分析区域对于销量的影响提出假设：0H :第i 区域的和第j 区域对销量没有显著性差异1H ：第i 区域和第j 区域对销量有显著性差异显著性水平为95% 自由度为126 >> tinv(0.025,126) ans = -1.9790LSD = 1.979*11.46=决策：当|i j x x - |>LSD 时，拒绝0H ,当|i j x x - |<LSD ，不决绝0H使用SPSS软件的LSD分析可以得到下表多重比较因变量: VAR00015LSD(I) VAR00011 (J) VAR00011 均值差(I-J) 标准误显著性95% 置信区间下限上限1.002.00 -4.37500 5.79135 .451 -15.8359 7.08593.00 -21.00000* 5.79135 .000 -32.4609 -9.53914.00 -19.25000*5.79135 .001 -30.7109 -7.78915.00 -12.62500* 5.79135 .031 -24.0859 -1.16416.00 -6.37500 5.79135 .273 -17.8359 5.08597.00 1.25000 5.79135 .829 -10.2109 12.71098.00 -13.37500* 5.79135 .023 -24.8359 -1.91419.00 2.37500 5.79135 .682 -9.0859 13.835910.00 -17.75000* 5.79135 .003 -29.2109 -6.289111.00 7.75000 5.79135 .183 -3.7109 19.210912.00 -9.75000 5.79135 .095 -21.2109 1.710913.00 -7.00000 5.79135 .229 -18.4609 4.460914.00 -4.12500 5.79135 .478 -15.5859 7.335915.00 -7.00000 5.79135 .229 -18.4609 4.460916.00 -9.25000 5.79135 .113 -20.7109 2.210917.00 6.12500 5.79135 .292 -5.3359 17.585918.00 -8.37500 5.79135 .151 -19.8359 3.08592.00 1.00 4.37500 5.79135 .451 -7.0859 15.83593.00 -16.62500* 5.79135 .005 -28.0859 -5.16414.00 -14.87500*5.79135 .011 -26.3359 -3.41415.00 -8.25000 5.79135 .157 -19.7109 3.21096.00 -2.00000 5.79135 .730 -13.4609 9.46097.00 5.62500 5.79135 .333 -5.8359 17.08598.00 -9.00000 5.79135 .123 -20.4609 2.46099.00 6.75000 5.79135 .246 -4.7109 18.210910.00 -13.37500* 5.79135 .023 -24.8359 -1.914111.00 12.12500* 5.79135 .038 .6641 23.585912.00 -5.37500 5.79135 .355 -16.8359 6.085913.00 -2.62500 5.79135 .651 -14.0859 8.835914.00 .25000 5.79135 .966 -11.2109 11.710915.00 -2.62500 5.79135 .651 -14.0859 8.835916.00 -4.87500 5.79135 .402 -16.3359 6.585917.00 10.50000 5.79135 .072 -.9609 21.960918.00 -4.00000 5.79135 .491 -15.4609 7.46093.00 1.00 21.00000* 5.79135 .000 9.5391 32.46092.00 16.62500* 5.79135 .005 5.1641 28.08594.00 1.750005.79135 .763 -9.7109 13.21095.00 8.37500 5.79135 .151 -3.0859 19.83596.00 14.62500* 5.79135 .013 3.1641 26.08597.00 22.25000* 5.79135 .000 10.7891 33.71098.00 7.62500 5.79135 .190 -3.8359 19.08599.00 23.37500* 5.79135 .000 11.9141 34.835910.00 3.25000 5.79135 .576 -8.2109 14.710911.00 28.75000* 5.79135 .000 17.2891 40.210912.00 11.25000 5.79135 .054 -.2109 22.710913.00 14.00000* 5.79135 .017 2.5391 25.460914.00 16.87500* 5.79135 .004 5.4141 28.335915.00 14.00000* 5.79135 .017 2.5391 25.460916.00 11.75000* 5.79135 .045 .2891 23.210917.00 27.12500* 5.79135 .000 15.6641 38.585918.00 12.62500* 5.79135 .031 1.1641 24.08594.00 1.00 19.25000*5.79135 .001 7.7891 30.71092.00 14.87500* 5.79135 .0113.4141 26.33593.00 -1.75000 5.79135 .763 -13.2109 9.71095.006.62500 5.79135 .255 -4.8359 18.08596.00 12.87500* 5.79135 .028 1.4141 24.33597.00 20.50000* 5.79135 .001 9.0391 31.96098.00 5.87500 5.79135 .312 -5.5859 17.33599.00 21.62500* 5.79135 .000 10.1641 33.085910.00 1.50000 5.79135 .796 -9.9609 12.960911.00 27.00000* 5.79135 .000 15.5391 38.460912.00 9.50000 5.79135 .103 -1.9609 20.960913.00 12.25000* 5.79135 .036 .7891 23.710914.00 15.12500* 5.79135 .010 3.6641 26.585915.00 12.25000* 5.79135 .036 .7891 23.710916.00 10.00000 5.79135 .087 -1.4609 21.460917.00 25.37500* 5.79135 .000 13.9141 36.835918.00 10.87500 5.79135 .063 -.5859 22.33595.00 1.00 12.62500* 5.79135 .031 1.1641 24.08592.00 8.25000 5.79135 .157 -3.2109 19.71093.00 -8.37500 5.79135 .151 -19.8359 3.08594.00 -6.625005.79135 .255 -18.0859 4.83596.00 6.25000 5.79135 .283 -5.2109 17.71097.00 13.87500* 5.79135 .018 2.4141 25.33598.00 -.75000 5.79135 .897 -12.2109 10.71099.00 15.00000* 5.79135 .011 3.5391 26.460910.00 -5.12500 5.79135 .378 -16.5859 6.335911.00 20.37500* 5.79135 .001 8.9141 31.835912.00 2.87500 5.79135 .620 -8.5859 14.335913.00 5.62500 5.79135 .333 -5.8359 17.085914.00 8.50000 5.79135 .145 -2.9609 19.960915.00 5.62500 5.79135 .333 -5.8359 17.085916.00 3.37500 5.79135 .561 -8.0859 14.835917.00 18.75000* 5.79135 .002 7.2891 30.210918.00 4.25000 5.79135 .464 -7.2109 15.71096.00 1.00 6.37500 5.79135 .273 -5.0859 17.83592.00 2.00000 5.79135 .730 -9.4609 13.46093.00 -14.62500*5.79135 .013 -26.0859 -3.16414.00 -12.87500*5.79135 .028 -24.3359 -1.41415.00 -6.25000 5.79135 .283 -17.7109 5.21097.00 7.62500 5.79135 .190 -3.8359 19.08598.00 -7.00000 5.79135 .229 -18.4609 4.46099.00 8.75000 5.79135 .133 -2.7109 20.210910.00 -11.37500 5.79135 .052 -22.8359 .085911.00 14.12500* 5.79135 .016 2.6641 25.585912.00 -3.37500 5.79135 .561 -14.8359 8.085913.00 -.62500 5.79135 .914 -12.0859 10.835914.00 2.25000 5.79135 .698 -9.2109 13.710915.00 -.62500 5.79135 .914 -12.0859 10.835916.00 -2.87500 5.79135 .620 -14.3359 8.585917.00 12.50000* 5.79135 .033 1.0391 23.960918.00 -2.00000 5.79135 .730 -13.4609 9.46097.00 1.00 -1.25000 5.79135 .829 -12.7109 10.21092.00 -5.62500 5.79135 .333 -17.0859 5.83593.00 -22.25000* 5.79135 .000 -33.7109 -10.78914.00 -20.50000*5.79135 .001 -31.9609 -9.03915.00 -13.87500* 5.79135 .018 -25.3359 -2.41416.00 -7.62500 5.79135 .190 -19.0859 3.83598.00 -14.62500* 5.79135 .013 -26.0859 -3.16419.00 1.12500 5.79135 .846 -10.3359 12.585910.00 -19.00000* 5.79135 .001 -30.4609 -7.539111.00 6.50000 5.79135 .264 -4.9609 17.960912.00 -11.00000 5.79135 .060 -22.4609 .460913.00 -8.25000 5.79135 .157 -19.7109 3.210914.00 -5.37500 5.79135 .355 -16.8359 6.085915.00 -8.25000 5.79135 .157 -19.7109 3.210916.00 -10.50000 5.79135 .072 -21.9609 .960917.00 4.87500 5.79135 .402 -6.5859 16.335918.00 -9.62500 5.79135 .099 -21.0859 1.83598.00 1.00 13.37500* 5.79135 .023 1.9141 24.83593.00 -7.62500 5.79135 .190 -19.0859 3.83594.00 -5.87500 5.79135 .312 -17.3359 5.58595.00 .75000 5.79135 .897 -10.7109 12.21096.007.00000 5.79135 .229 -4.4609 18.46097.00 14.62500* 5.79135 .013 3.1641 26.08599.00 15.75000* 5.79135 .007 4.2891 27.210910.00 -4.37500 5.79135 .451 -15.8359 7.085911.00 21.12500* 5.79135 .000 9.6641 32.585912.00 3.62500 5.79135 .532 -7.8359 15.085913.00 6.37500 5.79135 .273 -5.0859 17.835914.00 9.25000 5.79135 .113 -2.2109 20.710915.00 6.37500 5.79135 .273 -5.0859 17.835916.00 4.12500 5.79135 .478 -7.3359 15.585917.00 19.50000* 5.79135 .001 8.0391 30.960918.00 5.00000 5.79135 .390 -6.4609 16.46099.00 1.00 -2.37500 5.79135 .682 -13.8359 9.08592.00 -6.75000 5.79135 .246 -18.2109 4.71093.00 -23.37500* 5.79135 .000 -34.8359 -11.91414.00 -21.62500*5.79135 .000 -33.0859 -10.16415.00 -15.00000* 5.79135 .011 -26.4609 -3.53916.00 -8.75000 5.79135 .133 -20.2109 2.71097.00 -1.12500 5.79135 .846 -12.5859 10.33598.00 -15.75000* 5.79135 .007 -27.2109 -4.289110.00 -20.12500* 5.79135 .001 -31.5859 -8.664111.00 5.37500 5.79135 .355 -6.0859 16.835912.00 -12.12500* 5.79135 .038 -23.5859 -.664113.00 -9.37500 5.79135 .108 -20.8359 2.085914.00 -6.50000 5.79135 .264 -17.9609 4.960915.00 -9.37500 5.79135 .108 -20.8359 2.085916.00 -11.62500* 5.79135 .047 -23.0859 -.164117.00 3.75000 5.79135 .518 -7.7109 15.210918.00 -10.75000 5.79135 .066 -22.2109 .710910.00 1.00 17.75000* 5.79135 .003 6.2891 29.21092.00 13.37500* 5.79135 .023 1.9141 24.83593.00 -3.25000 5.79135 .576 -14.7109 8.21094.00 -1.500005.79135 .796 -12.9609 9.96095.00 5.12500 5.79135 .378 -6.3359 16.58596.00 11.37500 5.79135 .052 -.0859 22.83597.00 19.00000* 5.79135 .001 7.5391 30.46098.00 4.37500 5.79135 .451 -7.0859 15.83599.00 20.12500* 5.79135 .001 8.6641 31.5859 11.00 25.50000* 5.79135 .000 14.0391 36.960913.00 10.75000 5.79135 .066 -.7109 22.210914.00 13.62500* 5.79135 .020 2.1641 25.085915.00 10.75000 5.79135 .066 -.7109 22.210916.00 8.50000 5.79135 .145 -2.9609 19.960917.00 23.87500* 5.79135 .000 12.4141 35.335918.00 9.37500 5.79135 .108 -2.0859 20.835911.00 1.00 -7.75000 5.79135 .183 -19.2109 3.71092.00 -12.12500* 5.79135 .038 -23.5859 -.66413.00 -28.75000* 5.79135 .000 -40.2109 -17.28914.00 -27.00000*5.79135 .000 -38.4609 -15.53915.00 -20.37500* 5.79135 .001 -31.8359 -8.91416.00 -14.12500* 5.79135 .016 -25.5859 -2.66417.00 -6.50000 5.79135 .264 -17.9609 4.96098.00 -21.12500* 5.79135 .000 -32.5859 -9.66419.00 -5.37500 5.79135 .355 -16.8359 6.085910.00 -25.50000* 5.79135 .000 -36.9609 -14.039112.00 -17.50000* 5.79135 .003 -28.9609 -6.039113.00 -14.75000* 5.79135 .012 -26.2109 -3.289114.00 -11.87500* 5.79135 .042 -23.3359 -.414115.00 -14.75000* 5.79135 .012 -26.2109 -3.289116.00 -17.00000* 5.79135 .004 -28.4609 -5.539117.00 -1.62500 5.79135 .779 -13.0859 9.835918.00 -16.12500* 5.79135 .006 -27.5859 -4.664112.00 1.00 9.75000 5.79135 .095 -1.7109 21.21092.00 5.37500 5.79135 .355 -6.0859 16.83593.00 -11.25000 5.79135 .054 -22.7109 .21094.00 -9.500005.79135 .103 -20.9609 1.96095.00 -2.87500 5.79135 .620 -14.3359 8.58596.00 3.37500 5.79135 .561 -8.0859 14.83597.00 11.00000 5.79135 .060 -.4609 22.46098.00 -3.62500 5.79135 .532 -15.0859 7.83599.00 12.12500* 5.79135 .038 .6641 23.585910.00 -8.00000 5.79135 .170 -19.4609 3.460911.00 17.50000* 5.79135 .003 6.0391 28.960913.00 2.75000 5.79135 .636 -8.7109 14.210914.00 5.62500 5.79135 .333 -5.8359 17.085915.00 2.75000 5.79135 .636 -8.7109 14.210916.00 .50000 5.79135 .931 -10.9609 11.960917.00 15.87500* 5.79135 .007 4.4141 27.335918.00 1.37500 5.79135 .813 -10.0859 12.835913.00 1.00 7.00000 5.79135 .229 -4.4609 18.46092.00 2.62500 5.79135 .651 -8.8359 14.08594.00 -12.25000*5.79135 .036 -23.7109 -.78915.00 -5.62500 5.79135 .333 -17.0859 5.83596.00 .62500 5.79135 .914 -10.8359 12.08597.00 8.25000 5.79135 .157 -3.2109 19.71098.00 -6.37500 5.79135 .273 -17.8359 5.08599.00 9.37500 5.79135 .108 -2.0859 20.835910.00 -10.75000 5.79135 .066 -22.2109 .710911.00 14.75000* 5.79135 .012 3.2891 26.210912.00 -2.75000 5.79135 .636 -14.2109 8.710914.00 2.87500 5.79135 .620 -8.5859 14.335915.00 .00000 5.79135 1.000 -11.4609 11.460916.00 -2.25000 5.79135 .698 -13.7109 9.210917.00 13.12500* 5.79135 .025 1.6641 24.585918.00 -1.37500 5.79135 .813 -12.8359 10.085914.00 1.00 4.12500 5.79135 .478 -7.3359 15.58592.00 -.25000 5.79135 .966 -11.7109 11.21093.00 -16.87500* 5.79135 .004 -28.3359 -5.41414.00 -15.12500* 5.79135 .010 -26.5859 -3.66415.00 -8.50000 5.79135 .145 -19.9609 2.96096.00 -2.25000 5.79135 .698 -13.7109 9.21097.00 5.37500 5.79135 .355 -6.0859 16.83598.00 -9.25000 5.79135 .113 -20.7109 2.21099.00 6.50000 5.79135 .264 -4.9609 17.960910.00 -13.62500* 5.79135 .020 -25.0859 -2.164111.00 11.87500* 5.79135 .042 .4141 23.335912.00 -5.62500 5.79135 .333 -17.0859 5.835913.00 -2.87500 5.79135 .620 -14.3359 8.585915.00 -2.87500 5.79135 .620 -14.3359 8.585916.00 -5.12500 5.79135 .378 -16.5859 6.335917.00 10.25000 5.79135 .079 -1.2109 21.710918.00 -4.25000 5.79135 .464 -15.7109 7.210915.00 1.00 7.00000 5.79135 .229 -4.4609 18.46092.00 2.62500 5.79135 .651 -8.8359 14.08593.00 -14.00000*5.79135 .017 -25.4609 -2.53914.00 -12.25000*5.79135 .036 -23.7109 -.78915.00 -5.62500 5.79135 .333 -17.0859 5.83596.00 .62500 5.79135 .914 -10.8359 12.08597.00 8.25000 5.79135 .157 -3.2109 19.71098.00 -6.37500 5.79135 .273 -17.8359 5.08599.00 9.37500 5.79135 .108 -2.0859 20.835910.00 -10.75000 5.79135 .066 -22.2109 .710911.00 14.75000* 5.79135 .012 3.2891 26.210912.00 -2.75000 5.79135 .636 -14.2109 8.710913.00 .00000 5.79135 1.000 -11.4609 11.460914.00 2.87500 5.79135 .620 -8.5859 14.335916.00 -2.25000 5.79135 .698 -13.7109 9.210917.00 13.12500* 5.79135 .025 1.6641 24.585918.00 -1.37500 5.79135 .813 -12.8359 10.085916.00 1.00 9.25000 5.79135 .113 -2.2109 20.71092.00 4.87500 5.79135 .402 -6.5859 16.33593.00 -11.75000* 5.79135 .045 -23.2109 -.28914.00 -10.000005.79135 .087 -21.4609 1.46095.00 -3.37500 5.79135 .561 -14.8359 8.08596.00 2.87500 5.79135 .620 -8.5859 14.33597.00 10.50000 5.79135 .072 -.9609 21.96098.00 -4.12500 5.79135 .478 -15.5859 7.33599.00 11.62500* 5.79135 .047 .1641 23.085910.00 -8.50000 5.79135 .145 -19.9609 2.960911.00 17.00000* 5.79135 .004 5.5391 28.460912.00 -.50000 5.79135 .931 -11.9609 10.960913.00 2.25000 5.79135 .698 -9.2109 13.710914.00 5.12500 5.79135 .378 -6.3359 16.585915.00 2.25000 5.79135 .698 -9.2109 13.710917.00 15.37500* 5.79135 .009 3.9141 26.835918.00 .87500 5.79135 .880 -10.5859 12.335917.00 1.00 -6.12500 5.79135 .292 -17.5859 5.33592.00 -10.50000 5.79135 .072 -21.9609 .96093.00 -27.12500* 5.79135 .000 -38.5859 -15.66414.00 -25.37500* 5.79135 .000 -36.8359 -13.91415.00 -18.75000* 5.79135 .002 -30.2109 -7.28916.00 -12.50000* 5.79135 .033 -23.9609 -1.03917.00 -4.87500 5.79135 .402 -16.3359 6.58598.00 -19.50000* 5.79135 .001 -30.9609 -8.03919.00 -3.75000 5.79135 .518 -15.2109 7.710910.00 -23.87500* 5.79135 .000 -35.3359 -12.414111.00 1.62500 5.79135 .779 -9.8359 13.085912.00 -15.87500* 5.79135 .007 -27.3359 -4.414113.00 -13.12500* 5.79135 .025 -24.5859 -1.664114.00 -10.25000 5.79135 .079 -21.7109 1.210915.00 -13.12500* 5.79135 .025 -24.5859 -1.664116.00 -15.37500* 5.79135 .009 -26.8359 -3.9141 18.00 -14.50000* 5.79135 .014 -25.9609 -3.039118.00 1.00 8.37500 5.79135 .151 -3.0859 19.83592.00 4.00000 5.79135 .491 -7.4609 15.46093.00 -12.62500* 5.79135 .031 -24.0859 -1.16414.00 -10.875005.79135 .063 -22.3359 .58595.00 -4.25000 5.79135 .464 -15.7109 7.21096.00 2.00000 5.79135 .730 -9.4609 13.46097.00 9.62500 5.79135 .099 -1.8359 21.08598.00 -5.00000 5.79135 .390 -16.4609 6.46099.00 10.75000 5.79135 .066 -.7109 22.210910.00 -9.37500 5.79135 .108 -20.8359 2.085911.00 16.12500* 5.79135 .006 4.6641 27.585912.00 -1.37500 5.79135 .813 -12.8359 10.085913.00 1.37500 5.79135 .813 -10.0859 12.835914.00 4.25000 5.79135 .464 -7.2109 15.710915.00 1.37500 5.79135 .813 -10.0859 12.835916.00 -.87500 5.79135 .880 -12.3359 10.585917.00 14.50000* 5.79135 .014 3.0391 25.9609 *. 均值差的显著性水平为 0.05。