MBA-MARKETING.ppt
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1、Relationship among variables v Functional relationship v Statistical relationship(correlation) Y depends on X, but isnt merely determined by X. Example: price and sales daily high temperaturethe demand for air-conditioning v RegressionAccording to observed data, establish regression equation and mak
2、e statistical reference (predict) . Chapter 10 (P 227) Correlation and Regression Analysis 1 What does regression do? Solve the following problems: qDetermine whether there is statistical relationship among variables, if does, give the regression equation. qForecast the value of another variable (de
3、pendent) according to one variable or a group of variables (independent). 2 Example: X-price,Y-sales for a kind of product We collect data: 1. Scatter plot 2. Regression equation(the Least Square Estimation) 3. Correlation coefficient (Testing the regression model) 4.Forecasting (point and interval
4、forecasting ) Simple Linear Regression X(Yuan)708090100110 Y(thousand)11.2511.2811.6511.7012.14 3 Linear Regression Model Variables consist of a linear function. YX iii 01 Slope Y-Intercept Independent (Explanatory) Variable Dependent (Response) Variable Random Error 4 Sample Linear Regression Model
5、 ei = random error Y X Ybb Xe i ii 01 Ybb X ii 01 Sampled Observed Value 5 Sample Linear Regression Model The least squares method provides an estimated regression equation that minimizes the sum of squared deviations between the observed values of the dependent variable yi and the estimated values
6、of the dependent variable . 6 Least Squares estimation e2 Y X e1 e3 e4 Ybb Xe iii01 Ybb X ii01 OLS Min eeeee i i 2 1 1 2 2 2 3 2 4 2 Predicted Value 7 Coefficient & Equation Y bX b X YnXY Xn X bYb X ii ii i n i i n 01 1 1 2 2 1 01 Sample regression equation Slope for the estimated regression equatio
7、n P 238 (10.17) Intercept for the estimated regression equation b 8 Evaluating the Model q Significance Test q Test Coefficient of Determination and Standard Deviation of Estimation q Residual Analysis Y b bX ii 01 9 Measures of Variation in Regression SST = SSR + SSE 1. Total Sum of Squares (SST) P
8、 239 (10.20) Measure the variation between the observed value Yi and the mean Y. 2. Sum of Squares due to Regression (SSR) Variation caused by the relationship between X and Y. 3. Sum of Squares due to Error (SSE) Variation caused by other factors. 10 Variation Measures Y X Y Xi SST (Yi - Y)2 SSE (Y
9、i -Yi)2 SSR (Yi - Y)2 Yi Ybb X ii 01 11 Coefficient of Determination 0 r2 1 r bYbX Yn Y Yn Y iii i n i n i i n 2 01 2 11 2 1 2 Explained variation Total variation SSR SST A measure of the goodness of fit of the estimated regression equation. It can be interpreted as the proportion of the variation i
10、n the dependent variable y that is explained by the estimated regression equation. 12 Correlation Coefficient A numerical measure of linear association between two variables that takes values between 1 and +1. Values near +1 indicate a strong positive linear relationship, values near 1 indicate a st
11、rong negative linear relationship, and values near zero indicate lack of a linear relationship. 13 Coefficients of Determination (r2) and Correlation (r) r2 = 1, r2 = 0,Y Yi = b0 + b1Xi X Y Yi = b0 + b1Xi X Y Yi = b0 + b1Xi X Y Yi = b0 + b1Xi X r = +1 r = -1 r = +0.9r = 0 14 Test of Slope Coefficien
12、t for Significance 1. Tests a Linear Relationship Between X & Y 2. Hypotheses H0: 1 = 0 (No Linear Relationship) H1: 1 0 (Linear Relationship) 3. Test Statistic 15 Example Test of Slope Coefficient H0: 1 = 0 H1: 1 0 .05 df 5 - 2 = 3 Critical value: Statistic: Determine: Conclusion: t b Sb 11 1 0700
13、01915 3655 . . . Reject at = 0.05 There is evidence of a relationship. t 0 3.1824-3.1824 .025 RejectReject .025 16 Multiple Regression Model There exists linear relationship among an dependent variable and two or more than two independent variables. YXXX iiiPPii 01122 slope of population intercept o
14、f population Y random error Dependent VariableIndependent Variables 17 Example: New York Times You work in the advertisement department of New York Times(NYT). You will find to what extent do ads size(square inch ) and publishing volume (thousand) influence the response to ads(hundred). You have col
15、lected the following data: response size volume 112 488 131 357 264 4106 18 Example (NYT) Computer Output Parameter Estimates Parameter Standard T for H0: Variable DF Estimate Error Param=0 Prob|T| INTERCEP 1 0.0640 0.2599 0.246 0.8214 ADSIZE 1 0.2049 0.0588 3.656 0.0399 CIRC 1 0.2805 0.0686 4.089 0
16、.0264 b2 b0 bP b1 19 Interpretation of Coefficients 1.Slope (b1) If the publishing volume remains unchanged,when ads size increases one square inch, the response is expected to increase 0.2049 hundred times. 2.Slope (b2) If ads size remains unchanged, when publishing volume increases one thousand, t
17、he response is expected to in- crease 0.2805 hundred times. 20 Evaluating the Model 1. How does the model describe the relationship among variables? 2. Closeness of Best Fit 3. Assumptions met 4. Significance of estimates 5. Correlation among variables 6. Outliers (unusual observations) 21 Testing O
18、verall Significance 1. Test whether there is linear relationship between Y and all the independent variables. 2. Use F statistic. 3. Hypothesis H0: 1 = 2 = . = P = 0 3. There is no linear relationship between Y and independent variables. H1: At least there is a coefficient isnt equal to 0. At least
19、there is an independent variable influences Y 22 Testing Overall Significance Computer Output Analysis of Variance Sum of Mean Source DF Squares Square F Value ProbF Model 2 9.2497 4.6249 55.440 0.0043 Error 3 0.2503 0.0834 C Total 5 9.5000 Pn - P -1 n - 1 MSR / MSE p Value 23 Transformations in Reg
20、ression Models qNon-linear models that can be transformed into linear models (convenient to carry out OLS). qData Transformation qMultiplicative Model Example YXX YXX iiii iiii 012 01122 12 lnlnlnlnln 24 Square-Root Transformation YXX iiii 01122 1 0 1 0 1 0 1 0 Y X1 27 价格策略与管理 (定价目标;定价策略) 成本定价策略成本定价
21、策略 市场定价策略市场定价策略 产品之定价方法与策略 选择定价目标 (1)维持生存(Survival) (2)最大当期利润(Maximum current profit) (3)最大当期收入(Maximum current revenue) (4)最大销售成长(Maximum sales growth) (5)最大市场吸脂(Maximum market skimming) (6)领先的产品品质(Product-quality) 订价的目的 (1)利润: 即订价不可低于其投资报酬的最低水准。 (2)竞争: 即订价不可太高,以避免竞争厂商产生诱因进 而扩充生产能量。 (3)市场占有率: 即订价尽可
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