多元回归分析张洋zuizhong.ppt

1、,张洋,多元回归分析,20114004037,multiple regression analysis,英国人类学家 F.Galton首次在自然遗传一书中，提出并阐明了“相关”和“相关系数”两个概念，为相关论奠定了基础。其后，他和英国统计学家 Karl Pearson对上千个家庭的身高做了测量，发现：,Background of Regression analysis,儿子身高（ Y，英寸）与父亲身高（X，英寸）存在线性关系Y =33.73+0.516 X ： 。 也即高个子父代的子代在成年之后的身高平均来说不是更高，而是稍矮于其父代水平，而矮个子父代的子代的平均身高不是更矮，而是稍高于其父代

2、水平。Galton将这种趋向于种族稳定的现象称之“回归”,Background of regression analysis,Simple regression VS Multiple regression,In simple regression(一元回归) we study the relationship between one explanatory variable and one response variable. Now, we look at situations where several explanatory variables works together to ex

3、plain the response.,Introduction of Multiple regression analysis,Multiple regression is at the heart of social science data analysis, because it deals with explanations and correlations. Multiple regression analysis tells us how much each of several independent variables contributes to predicting th

4、e score of a single dependent variable.,Introduction of Multiple regression analysis,We may estimate a persons weight according to his/her gender, age, and height.,Can you guess my weight?,Actually in our daily life, we often do such predicting.,Introduction of Multiple regression analysis,Example:

5、The yield of rice per acre depends upon quality of seed, fertility of soil, fertilizer used, temperature, rainfall. If one is interested to study the joint affect of all these variables on rice yield, one can use this technique. X1: quality of seed X2 : fertility of soil X3 : fertilizer used X4 : te

6、mperature X5 : rainfall The model for this example is Y=0+ 1x1+ 2x2+ 3x3+ 4x4+5x5 +,This year is a good harvest!,Introduction of Multiple regression analysis,General regression model Y=0+ 1x1+ 2x2+ + kxk+ 1, 2, , kare parameters X1, X2, ,Xk are known constants , the error terms are independent N(o,

7、2),Interpreting Regression Coefficients(回归系数),Y=0+ 1x1+ 2x2+ + kxk+ Here 0 is the intercept（截距） 1, 2, 3, , k are called regression coefficients. Thus if 1 = 2.5, it would indicates that Y will increase by 2.5 units if x1increased by 1 unit. The appropriateness of the multiple regression model as a w

8、hole can be tested by the F-test A significant F indicates a linear relationship between Y and at least one of the Xs.,How Good Is the Regression?,Once a multiple regression equation has been constructed, one can check how good it is (in terms of predictive ability) by examining the coefficient of deter