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# multivariate statistical analysis

multivariate statistical analysis

Questions 5, 7, 10, 11, 12 13 14

1.    Define multivariate statistical analysis.
Multivariate analysis refers to a set of methods that simultaneously analyze the relationship between related variables. A series of multivariate analysis performed

separately for each feature can lead to erroneous interpretations given to the correlation or interdependence of these variables is ignored.

2.    What is the variate in multivariate?  What is an example of a variate in multiple regression and in factor analysis?
“The variate is a mathematical way in which a set of variables can be represented with one equation. Variates are formed as a linear combination of variables, each

contributing to the overall meaning of the variate based upon an empirically derived weight” (p.583), According to Janet Hus, President of Sanrio Consumer tend to

purchase products that provide emotional connection. A sample of variate is nostalgia products. Nostalgia products can be measured in multiples variables in order to

determine if variables are related to reduce the number of factors that represent that variate.

3.    What is the distinction between dependence methods and interdependence methods?
Dependence methods assume that the variables analyzed are divided into two groups: the dependent variables and independent variables. The aim is to determine whether

the set of independent variables affecting all variables dependent and how. Interdependence methods do not distinguish between dependent and independent variables and

the objective is to identify which variables are related, how they are and why

4.    What is the GLM?  How can multiple regression and n-way ANOVA be described as GLM approaches?
The general linear model (GLM) is a variant of multivariate dependence techniques. GLM is used to model based on the effect of the fluctuations of the average

dependent variable process and the relation to the different variables “Fluctuations can come in the form of group means that differ from the overall mean as in ANOVA

or in the form of a significant slope coefficient as in regression”.(Zikmund, 2013, p.586)

5.    What are the steps in interpreting a multiple regression analysis result?  Can the same steps be used to interpret a univariate ANOVA model?

6.    A researcher dismisses a regression result because the model R2 was under 0.70.  Do you think this was necessarily wise?  Explain.
After examining R2 no cutoffs values exists. If the researcher was more interested in predicting than explain then the absolute value is important; however given that

this case does not specify the purpose of the researcher is not possibletodetermine whether or not to discard the results of the regression

7.    Return to the simple example of regression results for the toy company presented in the chapter.   Since the data come equally from Europe and Canada, does

this represent a potential source of variation that is not accounted for in the researcher’s model?  How could the researcher examine whether or not sales may be

dependent upon country?

Multiple regressions can be done by using independent variables and

a dummy variablecan be used to represent Canada

and Europe by using 0 and 1 respectively variable.

A factor loading indicate the strength of the correlated factors and is used to identify factors that explain a variety of results in different tests. For example,

intelligence research found that people who get a high score on a test of verbal ability also performs well on tests requiring verbal skills

9.    How does factor analysis allow for data reduction?

Factor analysis allow for data reduction by reducing the number of variables and detecting the relationship between variables to classify them.  Therefore, factor

analysis is applied as a data reduction or structure detection method

10.    How is the number of factors decided in most EFA programs?

11.    What is multi-dimensional scaling?  When might a researcher use this technique?

12.    What is cluster analysis?  When might a researcher use this technique?

13.    Name at least two multivariate techniques that can be useful in constructing perceptual maps.

14.    A researcher uses multiple regression to predict a client’s sales volume based on gross domestic product, personal income, disposable personal income,

unemployment, and the consumer price index. What problems might be anticipated with this multiple regression model?

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