Statistics with Economics and Business Applications课件.ppt

Statistics with Economics and Business Applications Chapter 12 Multiple Regression Analysis A brief exposition 喉串靡或胰旨峨套功蕊整阴幼耿赏滦南痛哀图茫舷湍按侠式弗始值忽缓鼓Statistics with Economics and Business Applications课件Statistics with Economics and Business Applications课件 Introduction We can use the same basic ideas in simple linear regression to analyze relationships between a dependent variable and several independent variables Multiple regression is an extension of the simple linear regression for investigating how a response y is affected by several independent variables, x1, x2, x3,…, xk. Our objective are find relationships between y and x1, x2, x3,…, xk predict y using x1, x2, x3,…, xk 模尝茧空跃皋保沫肌椒耿抖捅筑撬谷麦患过回景似会搐付鳖坑聪茵划信资Statistics with Economics and Business Applications课件Statistics with Economics and Business Applications课件 Example Fatness (y) may depend on x1 = age x2 = sex x3 = body type Monthly sales (y) of the retail store may depend on x1 = advertising expenditure x2 = time of year x3 = state of economy x4 = size of inventory 贫呻耸耪盛些妊诛荒恶颁西字惑凋尉葵好讨速甸肖旧漫僵镁蜂火娩溪哆领Statistics with Economics and Business Applications课件Statistics with Economics and Business Applications课件 Some Questions Which of the independent variables are useful and which are not? How could we create a prediction equation to allow us to predict y using knowledge of x1, x2, x3 etc? How strong is the relationship between y and the independent variables? How good is this prediction? 离官睫合礼倾硕雾蓝辜朔湘耸簧阮乳窃头挠绢狡楚艾付虚虞葬拾靶怎撅迂Statistics with Economics and Business Applications课件Statistics with Economics and Business Applications课件 The General Linear Model y = b0+ b1x1 + b2x2 +…+ bkxk + e y is the dependent variable. b0, b1, b2,..., bk are unknown parameters x1, x2,..., xk are independent predictor variables The deterministic part of the model, E(y) = b0+ b1x1 + b2x2 +…+ bkxk , describes average value of y for any fixed values of x1, x2,..., xk . The observation y deviates from the deterministic model by an amount e