【正文】 ??????qpppqqyxyxyxyxyxyxyxyxyx?????? 若 (x1,x2,… ， xp)’的 分量相互獨立 , 則協(xié)方差 矩陣 ， 除主對角線上的元素外均為零 ， 即 ?????????????????)v a r (000)v a r (000)v a r ()(21pxxxV a r??????x2）隨機向量 X的協(xié)方差矩陣 ?是非負定矩陣。 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 隨機向量 167。 Solution 2: Type of Scale a) Nominal scale For example, 15 – 25 years : Category A 26 – 35 years : Category B 36 – 50 years : Category C 50 + years : Category D Note that depending upon how it is used, the above scale can also be considered as an ordinal scale ? Ratio scale Age measured as the number of years a person has lived Solution 2: Type of Scale b) Ordinal scale : Rank the following criteria in order of their importance in selecting a grocery store for your shopping – (i) Location (ii) Prices (iii) Cleanliness (iv) Service (v) Product quality Interval scale: Rate the following criteria based on how important they are in helping you select a grocery store for your Location 1 2 3 4 5 Least Important Extremely Important Number of Dummy Variables for Nominal Scale Data OCCUPATION DUMMY VARIABLES D1 D2 Professional 1 0 Technical 0 1 Blue collar 0 0 Types of Multivariate Techniques ※ Dependence Techniques – variables are divided into dependent and independent. Dependence techniques attempt to explain or predict the dependent variable(s) on the basis of two or more independent variables. ※ Interdependence Techniques – all variables are analyzed simultaneously, with none being designated as either dependent or independent. The goal of interdependence techniques is to give meaning to a set of variables or seek to group things together. No one variable, or variable subset is to be predicted from the others or explained by them. Dependence Techniques 1. Multiple Regression (MR) 2. Discriminant Analysis (DA) √ 3. Multivariate Analysis of Variance (MANOVA) √ 4. Canonical Correlation Analysis (CCA) √ Interdependence techniques 1. Principal Components Analysis (PCA) √ 2. Factor Analysis (FA) √ 3. Cluster Analysis (CA) √ 4. Multidimensional Scaling (MDS) Multiple Regression ? Multiple Regression (MR) – the objective of MR is to predict changes in a single metric dependent variable in response to changes in several metric independent variables. A related technique is multiple correlation. ? General Form Y = X1 + X2 + X3 + …. +Xn , where Y and the X’s are metric variables Discriminant Analysis ? Discriminant Analysis (DA) – the objective of DA is to predict group membership for a single nonmetric dependent variable using several metric independent variables. Multivariate Analysis of Variance (MANOVA) ? simultaneously analyzes the relationship of 2 or more metric dependent variables and several nonmetric independent variables ? Provides a significance test of mean difference between groups for two or more dependent variables Canonical Correlation ? Canonical Correlation Analysis (CCA) simultaneously correlates several metric dependent variables and several metric independent variables. Note that this procedure can be considered an extension of MR, where there is only one metric dependent variable. College Performance Variables PreCollege Performance Variables Statistics I Statistics II Project … Mathematics Physics English .. Credit Usage Characteristics No. of credit cards Monthly Usage Family Size Family Ine Principal Components Analysis ? Principal Components Analysis (PCA) – used to reduce many original variables to a few linear binations of them that best represent the original data. Factor Analysis Source: Marketing Research Within a Changing Informational Environment, by Hair, Bush and Ortinau (2020, McGraw Hill) Factor Analysis ? Factor Analysis (FA) – used to analyze the interrelationships among a large number of variables and then explain these variables in terms of their mon, underlying dimension Cluster Analysis ? Cluster Analysis (CA) – used to classify a sample into several mutually exclusive groups based on similarities and differences among the sample ponents Multidimensional Scaling ? Multidimensional Scaling (MDS) – a technique used to transform similarity scalings into distances in a multidimensional space. 統(tǒng)計分析方法在經(jīng)濟統(tǒng)計中具體應(yīng)用領(lǐng)域 ? 對多個變量進行降維處理 ， 而選擇數(shù)目較少的變量子集合 ? 主要方法：主成分分析 、 因子分析 、 對應(yīng)分析等 。 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。 ? (v) Size of the car。 ? (iii) Price of the car。 Metric