香皂的销售量问题

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1、香皂的销售量问题组员：丛轶颖秦思思朱小丹香皂的销售量问题一．问题的提出在实际生产销售过程中，我们发现香皂的销售量与香皂的价格以及广告投入之间有很大的关系，不同的价格，不同的广告投入会导致销售量的不同。那么香皂的销售量与这两者有满足怎样的关系呢？现在我们收集了30个销售周期本公司香皂销售量、价格、广告费用，及同期其他厂家同类牙膏的平均售价.，并制成如下表格：本厂价格其他厂家价格广告费用价格差销售量x2^213.853.81.62-0.058.382.624423.7545.610.258.5131.472133.73.833.80.138.4814.4443.

2、84.256.530.459.2142.640953.653.753.150.18.279.922563.753.853.130.18.289.796973.824.256.630.439.143.956983.83.851.420.058.092.016493.74.256.720.559.2645.1584103.853.922.410.078.125.8081113.733.823.030.098.229.18091244.123.730.128.3113.9129134.254.44.010.158.3616.0801145.55.674.50.17

3、8.4320.25155.255.434.940.188.524.4036164.254.465.280.218.5727.8784173.874.115.540.248.6230.6916183.94.185.770.288.7533.2929193.954.265.960.318.7835.5216203.854.186.130.338.837.5769213.553.936.280.388.9139.4384223.824.236.410.418.9941.08812344.446.510.449.1442.3801243.584.056.590.47

4、9.1743.4281254.556.650.59.2344.2225263.784.36.70.529.3144.89273.94.476.740.579.4545.4276283.84.386.770.589.545.8329293.74.296.790.599.546.1041303.94.56.80.69.646.24二．问题的分析题中香皂的销售量受到价格以及广告投入这两者的影响，单独分析销售量与价格之间的关系，由作出散点图，我们发现它们呈线性关系；同理观察销售量与广告投入，可以发现销售量与广告投入的平方呈线性关系，因此，当两者共同作用时，我们建立了

5、以下模型。三．模型的主要符号变量说明y~公司香皂销售量x1其他厂家与本公司价格差x2~公司广告费用y~被解释变量（因变量）x1,x2~解释变量(回归变量,自变量)β,β1,β2,β3,β4~回归系数ε~随机误差（均值为零的正态分布随机变量）.四.基本模型的建立与问题的求解用EXCEL作出y与x1的散点图，如图所示：用EXCEL作出y与x2的散点图，如图所示：(1)假设x1,x2对y影响独立：设y=β+β1x1+β2x2+β3x2^2+ε由MATLAB解出回归系数，程序如下：>>x1=[-0.050.250.130.450.10.10.430.050.550.

6、070.090.120.150.170.180.210.240.280.310.330.380.410.440.470.50.520.570.580.590.6];>>x2=[1.625.613.86.533.153.136.631.426.722.413.033.734.014.54.945.285.545.775.966.136.286.416.516.596.656.76.746.776.796.8];>>x3=[2.624431.472114.4442.64099.92259.796943.95692.016445.15845.80819.18091

7、3.912916.080120.2524.403627.878430.691633.292935.521637.576939.438441.088142.380143.428144.222544.8945.427645.832946.104146.24];>>y=[8.388.518.489.218.278.289.18.099.268.128.228.318.368.438.58.578.628.758.788.88.918.999.149.179.239.319.459.59.59.6];>>savedatax1x2x3>>loaddata;>>t=on

8、es(30,1);>>x=[tx1'x2'x3'];