Bài giảng Phương pháp nghiên cứu
Hàm tương quan đa biến Business Statistics: A Decision-Mak ing Approach, 6e © 2005 Prentice-Hall, Inc Chap 14-1 Mục tiêu học tập Thông hiểu việc xây dựng mơ hình với việc phân tích đa biến Thực việc xây dựng hàm tương quan đa biến Phân tích lý giải kết hàm tương quan đa biến Thực phép kiểm định thống kê với hàm tương quan đa biến Business Statistics: A Decision-Mak ing Approach, 6e © 2005 Prentice-Hall, Inc Chap 14-2 Mơ hình hàm tương quan đa biến Hàm tương quan đám đông Y-intercept Population slopes Random Error y β0 β1x1 β2 x βk x k ε Hàm tương quan ước lượng Estimated (or predicted) value of y Estimated intercept Estimated slope coefficients ˆ y b0 b1x1 b2 x bk x k Business Statistics: A Decision-Mak ing Approach, 6e © 2005 Prentice-Hall, Inc Chap 14-3 Mơ hình hàm tương quan đa biến (trường hợp hai biến) Mơ hình hai biến y ˆ y b0 b1x1 b2 x x2 x1 Business Statistics: A Decision-Mak ing Approach, 6e © 2005 Prentice-Hall, Inc Chap 14-4 Mơ hình hàm tương quan đa biến (trường hợp hai biến) Hai biến y Quan sát thực tế ˆ y b0 b1x1 b2 x yi < < yi e = (y – y) x2i x1i x1 Business Statistics: A Decision-Mak ing Approach, 6e © 2005 Prentice-Hall, Inc x2 Hàm tương quan có độ xác ướclượng cao tối thiểu hóa tổng bình phương sai lệch: Chap 14-5 e2 Multiple Regression Assumptions Sai lệch (errors) hay phần dư (residuals): < e = (y – y) Giả thuyết Các sai lệch có phân phối chuẩn Bình qn sai lệch co giá trị Phương sai sai lệch cố định Các sai lệch hoàn toàn độc lập Business Statistics: A Decision-Mak ing Approach, 6e © 2005 Prentice-Hall, Inc Chap 14-6 Ma trận hệ số tương quan Ma trận hệ số tương quan biến phụ thuôc biến độc lập tính Excel: Tools / Data Analysis… / Correlation Kiểm tra độ tin cậy thống kê hệ số tương quan với phép kiểm định t Business Statistics: A Decision-Mak ing Approach, 6e © 2005 Prentice-Hall, Inc Chap 14-7 Ví dụ Một nhà sản xuất bánh nướng muốn đánh giá tác động giá quảng cáo đến sản lượng hàng bán Biến phụ thuộc: Sản lượng (Chiếc tuần) Biến độc lập: giá ($) chi phí quảng cáo (đơn vị $100/tuần) Thông tin thu thập liên tục 15 tuần Business Statistics: A Decision-Mak ing Approach, 6e © 2005 Prentice-Hall, Inc Chap 14-8 Hàm tương quan đa biến Week Pie Sales Price ($) Advertising ($100s) 350 5.50 3.3 460 7.50 3.3 350 8.00 3.0 430 8.00 4.5 350 6.80 3.0 380 7.50 4.0 430 4.50 3.0 470 6.40 3.7 450 7.00 3.5 10 490 5.00 4.0 11 340 7.20 3.5 12 300 7.90 3.2 13 440 5.90 4.0 14 450 5.00 3.5 15 300 7.00 2.7 Multiple regression model: Sales = b0 + b1 (Price) + b2 (Advertising) Correlation matrix: Pie Sales Pie Sales Price Advertising Business Statistics: A Decision-Mak ing Approach, 6e © 2005 Prentice-Hall, Inc Price Advertising -0.44327 0.55632 0.03044 Chap 14-9 Giải thích ý nghĩa hệ số tương quan (bi) bi Giá trị trung bình y thay đổi bi đơn vị gia tăng đơn vị Xi, giả định biến khác cố định Hằng số tương quan (b0) Giá trị trung bình y biến Xi Business Statistics: A Decision-Mak ing Approach, 6e © 2005 Prentice-Hall, Inc Chap 14-10 Testing for Significance: Quadratic Model Test for Overall Relationship F test statistic = MSR MSE Testing the Quadratic Effect Compare quadratic model y β0 β1x j β x ε j with the linear model y β β1x j ε Hypotheses H0: β2 = (No 2nd order polynomial term) HA: β2 (2nd order polynomial term is needed) Business Statistics: A Decision-Mak ing Approach, 6e © 2005 Prentice-Hall, Inc Chap 14-45 Higher Order Models y x If p = the model is a cubic form: j j y β β1x j β x β3 x ε Business Statistics: A Decision-Mak ing Approach, 6e © 2005 Prentice-Hall, Inc Chap 14-46 Interaction Effects Hypothesizes interaction between pairs of x variables Response to one x variable varies at different levels of another x variable Contains two-way cross product terms 2 y β0 β1x1 β2 x1 β3 x3 β4 x1x β5 x1 x Basic Terms Business Statistics: A Decision-Mak ing Approach, 6e © 2005 Prentice-Hall, Inc Interactive Terms Chap 14-47 Effect of Interaction Given: y β β1x β x β x 1x ε Without interaction term, effect of x1 on y is measured by β1 With interaction term, effect of x1 on y is measured by β1 + β3 x2 Effect changes as x2 increases Business Statistics: A Decision-Mak ing Approach, 6e © 2005 Prentice-Hall, Inc Chap 14-48 Interaction Example y = + 2x1 + 3x2 + 4x1x2 y where x = or (dummy variable) x2 = y = + 2x1 + 3(1) + 4x1(1) = + 6x1 12 x2 = y = + 2x1 + 3(0) + 4x1(0) = + 2x1 x1 0 0.5 1.5 Effect (slope) of x1 on y does depend on x2 value Business Statistics: A Decision-Mak ing Approach, 6e © 2005 Prentice-Hall, Inc Chap 14-49 Interaction Regression Model Worksheet Case, i yi x1i x2i x1i x2i : : : : 40 30 : multiply x1 by x2 to get x1x2, then run regression with y, x1, x2 , x1x2 Business Statistics: A Decision-Mak ing Approach, 6e © 2005 Prentice-Hall, Inc Chap 14-50 Evaluating Presence of Interaction Hypothesize interaction between pairs of independent variables y β β1x1 β x β x1x ε Hypotheses: H0: β = (no interaction between x1 and x2) HA: β ≠ (x1 interacts with x2) Business Statistics: A Decision-Mak ing Approach, 6e © 2005 Prentice-Hall, Inc Chap 14-51 Model Building Goal is to develop a model with the best set of independent variables Stepwise regression procedure Easier to interpret if unimportant variables are removed Lower probability of collinearity Provide evaluation of alternative models as variables are added Best-subset approach Try all combinations and select the best using the highest adjusted R2 and lowest sε Business Statistics: A Decision-Mak ing Approach, 6e © 2005 Prentice-Hall, Inc Chap 14-52 Stepwise Regression Idea: develop the least squares regression equation in steps, either through forward selection, backward elimination, or through standard stepwise regression The coefficient of partial determination is the measure of the marginal contribution of each independent variable, given that other independent variables are in the model Business Statistics: A Decision-Mak ing Approach, 6e © 2005 Prentice-Hall, Inc Chap 14-53 Best Subsets Regression Idea: estimate all possible regression equations using all possible combinations of independent variables Choose the best fit by looking for the highest adjusted R2 and lowest standard error sε Stepwise regression and best subsets regression can be performed using PHStat, Minitab, or other statistical software packages Business Statistics: A Decision-Mak ing Approach, 6e © 2005 Prentice-Hall, Inc Chap 14-54 Aptness of the Model Diagnostic checks on the model include verifying the assumptions of multiple regression: Each xi is linearly related to y Errors have constant variance Errors are independent Error are normally distributed Errors (or Residuals) are given by Business Statistics: A Decision-Mak ing Approach, 6e © 2005 Prentice-Hall, Inc ˆ ei ( y y ) Chap 14-55 residuals residuals Residual Analysis x Constant variance x Not Independent Business Statistics: A Decision-Mak ing Approach, 6e © 2005 Prentice-Hall, Inc residuals Non-constant variance residuals x x Independent Chap 14-56 The Normality Assumption Errors are assumed to be normally distributed Standardized residuals can be calculated by computer Examine a histogram or a normal probability plot of the standardized residuals to check for normality Business Statistics: A Decision-Mak ing Approach, 6e © 2005 Prentice-Hall, Inc Chap 14-57 Chapter Summary Developed the multiple regression model Tested the significance of the multiple regression model Developed adjusted R2 Tested individual regression coefficients Used dummy variables Examined interaction in a multiple regression model Business Statistics: A Decision-Mak ing Approach, 6e © 2005 Prentice-Hall, Inc Chap 14-58 Chapter Summary (continued) Described nonlinear regression models Described multicollinearity Discussed model building Stepwise regression Best subsets regression Examined residual plots to check model assumptions Business Statistics: A Decision-Mak ing Approach, 6e © 2005 Prentice-Hall, Inc Chap 14-59 ... tích đa biến Thực việc xây dựng hàm tương quan đa biến Phân tích lý giải kết hàm tương quan đa biến Thực phép kiểm định thống kê với hàm tương quan đa biến Business Statistics: A Decision-Mak... 2005 Prentice-Hall, Inc Chap 1 4-2 Mơ hình hàm tương quan đa biến Hàm tương quan đám đông Y-intercept Population slopes Random Error y β0 β1x1 β2 x βk x k ε Hàm tương quan ước lượng... định biến khác cố định Hằng số tương quan (b0) Giá trị trung bình y biến Xi Business Statistics: A Decision-Mak ing Approach, 6e © 2005 Prentice-Hall, Inc Chap 1 4-1 0 Kết hàm tương quan đa biến