Multiple regression, a time-honored technique going back to
Pearson's 1908 use of it, is employed to account for (predict) the variance in an interval dependent, based on linear
combinations of interval, dichotomous, or dummy independent
variables. Multiple regression can establish that a set of
independent variables explains a proportion of the variance in a dependent variable at a significant level (through a significance test of R2), and can establish the relative predictive importance of the independent variables (by comparing beta weights).

Power terms can be added as independent variables to explore curvilinear effects. Cross-product terms can be added as
independent variables to explore interaction effects. One can test the significance of difference of two R2's to determine if adding an independent variable to the model helps significantly. Using hierarchical regression, one can see how most variance in the dependent can be explained by one or a set of new

independent variables, over and above that explained by an
earlier set. Of course, the estimates (b coefficients and constant) can be used to construct a prediction equation and generate
predicted scores on a variable for further analysis.
The multiple regression equation takes the form y = b1x1 + b2x2 + ... + bnxn + c. The b's are the regression coefficients,
representing the amount the dependent variable y changes when the corresponding independent changes 1 unit. The c is the
constant, where the regression line intercepts the y axis,
representing the amount the dependent y will be when all the independent variables are 0. The standardized version of the b coefficients are the beta weights, and the ratio of the beta coefficients is the ratio of the relative predictive power of the independent variables. Associated with multiple regression is R2, multiple correlation, which is the percent of variance in the dependent variable explained collectively

...140
13 MultipleregressionMultipleregression
In this chapter I will briefly outline how to use SPSS for Windows to run multipleregression analyses. This is a very simplified outline. It is important that you do
more reading on multipleregression before using it in your own research. A good
reference is Chapter 5 in Tabachanick and Fiddell (2001), which covers the
underlying...

...Multipleregression: OLS method
(Mostly from Maddala)
The Ordinary Least Squares method of estimation can easily be extended to models involving two or more explanatory variables, though the algebra becomes progressively more complex. In fact, when dealing with the general regression problem with a large number of variables, we use matrix algebra, but that is beyond the scope of this course.
We illustrate the case of two explanatory...

...
Logistic regression
In statistics, logistic regression, or logit regression, is a type of probabilistic statistical classification model.[1] It is also used to predict a binary response from a binary predictor, used for predicting the outcome of acategorical dependent variable (i.e., a class label) based on one or more predictor variables (features). That is, it is used in estimating the parameters of a qualitative response model. The probabilities...

...Regression Analysis: A Complete Example
This section works out an example that includes all the topics we have discussed so far in this chapter.
A complete example of regression analysis.
PhotoDisc, Inc./Getty Images
A random sample of eight drivers insured with a company and having similar auto insurance policies was selected. The following table lists their driving experiences (in years) and monthly auto insurance premiums.
Driving Experience (years) Monthly...

...Topic 4. Multipleregression
Aims
• Explain the meaning of partial regression coefficient and calculate and interpret multipleregression models • Derive and interpret the multiple coefficient of determination R2and explain its relationship with the the adjusted R2 • Apply interval estimation and tests of significance to individual partial regression coefficients d d l ff • Test the...

...Chapter3
MultipleRegression Analysis: Estimation
Key drawback of SLR: all other factors affecting y are unrelated
with x, as is unrealistic.
Multipleregression allows us to control for many other
factors to explain dependent variable, which is useful both for
testing economic theories and for drawing the ceteris paribus
conclusion.
In addition, MR can incorporate fairly general functional form and
build better models for predicting...

...Regression Analysis (Tom’s Used Mustangs)
Irving Campus
GM 533: Applied Managerial Statistics
04/19/2012
Memo
To:
From:
Date: April 19st, 2012
Re: Statistic Analysis on price settings
Various hypothesis tests were compared as well as several multipleregressions in order to identify the factors that would manipulate the selling price of Ford Mustangs. The data being used contains observations on 35 used Mustangs and 10...

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