【正文】 eeking) needed. If the relationship is dependence based, the analyst must first determine the number of dependent and independent variables. Second, the analyst must determine how the dependent and independent variables will be measured. In selecting among the interdependence techniques, the analyst must define whether structure among variables, respondents or objects is desired Question: Which Multivariate Method to Use? A marketing research pany believes that the sales (S) of a product are a function of the number of retail outlets (NR) in which it is available, the advertising dollars (A) spent on the product, and the number of years (Ng) the product has already been available on the market. The pany has information on S, NR, A, and Ng for 35 peting brands at a given point in time. Suggest a suitable statistical method that will help the pany test the relationship between sales and NR, A, and Ng . Question: Which Multivariate Method to Use? In a nationwide survey of its customers, a leading marketer of consumer packaged goods collected information about various buying habits. The pany wants to identify distinct segments among the consumers and design marketing strategies tailored to individual segments. Suggest a suitable statistical method to the marketing research department of the pany to help it acplish this task. Question: Which Multivariate Method to Use? A market research pany wants to study whether ine level and the extent of advertising of the brands influence consumers in deciding which of the three brands of coffee to purchase. Suppose ine data collected from purchasers of these three brands of coffee and the extent of advertising can be measured on a metric scale. Which multivariate technique would you use to help predict the brand choice decision of consumers? Question: Which Multivariate Method to Use? ABC Tour amp。 ? (vi) Automatic v. stick shift。 ? (ii) Terms of payment。 the study of the relationships that exist among career performance, academic achievement, and aptitude test scores ? 167。 ? 主要內(nèi)容 ? 從形式上看，一類是 單變量 常用的統(tǒng)計方法在多維 隨機(jī)變量情況 下的應(yīng)用 ；另一類是對 多維變量 本身 進(jìn)行研究的一些 特殊方法 。 Problem Objectives amp。 Hypotheses Sample Experiment How to measure? Interpretation Knowledge Base DATA Conclusions Graphical Depiction of Scientific Study DESIGN Constraints STATISTICAL ANALYSIS Graphics amp。 Univariate versus Multivariate Analysis ? Univariate analysis ? Solely interested in an isolated characteristic of a set of objects, irrespective of other variable characteristics possessed by the objects ? Examples ? 167。 the study of the relationships among product sales, pricing, and advertising levels 一元統(tǒng)計與多元統(tǒng)計簡單比較 主要內(nèi)容 一元 多元 隨機(jī)變量 一維隨機(jī)變量 多維隨機(jī)變量 統(tǒng)計分布 一元分布 多元分布 參數(shù)估計 似然估計、最小二乘估 計、矩估計 似然估計、最小二乘 估計、矩估計 假設(shè)檢驗(yàn) U檢驗(yàn)、 t檢驗(yàn)、 F檢驗(yàn) 卡方檢驗(yàn) T2檢驗(yàn)、 F檢驗(yàn) 卡方檢驗(yàn) 統(tǒng)計分析方法 方差分析 回歸分析 回歸分析 主成分分析 因子分析 聚類分析 判別分析 典型相關(guān)分析等 具體內(nèi)容包括 ? 多元回歸分析 ? 主成分分析 ? 因子分析 ? 聚類分析 ? 判別分析 ? 對應(yīng)分析 ? 典型相關(guān)分析 ? 時間序列分析 ? 馬爾科夫概型分析 Types of Measurement Scales ? All measurement scales can be classified into the following four types: ?167。 ? (iii) Price of the car。 and ? (vii) Number of miles to a gallon of gas. (e) In a weightreduction program the weight (in pounds) Example 2: Type of Scale ? For each variable listed, certain measurement scales are indicated. In each case suggest suitable operational ? measures of the indicated scale type(s). (a) Age: nominal, ratio scales。 Travel Company advertises its tour packages by mailing brochures about tourist resorts. The pany feels it could increase its marketing efficiency if it were able to segregate consumers likely to go on its tours from those not likely to go, based on consumer demographics and lifestyle considerations. You decide to help the pany by undertaking some consumer research. From the pany’s files you extract the names and addresses of consumers who had received the brochures in the past two years. You select two random samples of consumers who went on the tours and those who didn’t. Having done this, you interview the selected consumers and collect demographic and lifestyle information (using nonmetric scales) about them. Describe a statistical method that you would use to help predict the tourgoing potential of consumers based on their demographics and lifestyles 第一章 隨機(jī)向量 167。兩隨機(jī)向量相互獨(dú)立若 0yx ?),(?167。 1 多元正態(tài)分布的定義 一 、 標(biāo)準(zhǔn)多元正態(tài)分布 設(shè)隨機(jī)向量 , 獨(dú)立同分布于 ， 則的 密度函數(shù)為 ),( 21 ?? puuu ?upuuu , 21 ?)1,0(N),( 21 ?? puuuu????????? pi ipinipxxxxxf1222121)21e x p ()2()21e x p (21),( ????????? ix pi ,2,1 ??其中的 均值為 ),( 21 ?? puuu ?u 0),()( 21 ??? pEuEuEuE ?u???????????????2212221212121)()(pppppuuuuuuuuuuuuuuuEV ar??????uuEu 協(xié)方差為 I??????????????111? 二、一般的正態(tài)分布 )]()(21e x p [)2(),( 121221 ??? ??????? ??? xxxxxf pp??????? ix其中 的均值為 ),( 21 ?? pxxx ?x ),()( 21 ?? pE ??? ?x協(xié)方差為 ????????????????????????????22211222222122112211211)())(())(())(()())(())(())(()(pppppppppxxxxxxxxxxxxxxxE??????????????????????),( 21 ?? pxxx ?x稱 服從均值為 E(X)， 協(xié)方差為 ?的正態(tài)分布 。 2 多元正態(tài)分布的性質(zhì) 二 、 x是一個服從 p維正態(tài)分布 ， 當(dāng)且僅當(dāng)它的任何 線性函數(shù) 服從一元正態(tài)分布 。（服從維標(biāo)準(zhǔn)正態(tài)分布，故是 )2*39。 ),(~ I0Nx n ??? Axy ??? Bxz Anp? B nq? pArank ?)( qBra n k ?)(YZ 0??BA))(()c o v ( ???? zzyyzy, EEE?)( ???? BxA x) ( B xAx EEEBxx) ( xxA ????? )( EEEBxA ?? )(V arBAI ??BA ?? 九、設(shè)