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Chapter 1

PSYC09H3 Chapter Notes - Chapter 1: Confidence Interval, Sampling Error, Observational Error

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Douglas Bors

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Chapter 1: Multiple Regression
Majorly used for prediction and casual analysis
Casual analysis: independent variables are regarded as causes of criterion (dependent
variable) determine whether a particular independent variable really affects the
dependent variable, and to estimate the magnitude of that effect, if any
Multiple regression: statistical method for studying the relationship between a single
dependent variable (criterion) and one or more independent (predictor) variables
Other Names for Multiple Regression
Ordinary least squares multiple regression
Ordinary = simple
Least squares = method used to estimate the regression equation
Multiple = two or more independent variables
Linear = kind of equation that is estimated by the multiple regression method
Regression = “regression to the mean”
Why Multiple Regression?
For prediction studies, multiple regression makes it possible to combine many variables
to produce optimal predictions of the dependent variable
For casual analysis, multiple regression separates the effects of independent variables on
the dependent variable so that you can examine the unique contribution of each variable
Why Is Regression Linear?
Means it is based on a linear equation if you graph the equation you should get a
straight line
Method of least squares is designed to find numbers that give us optimal predictions of
the dependent variable
Y = a + bx two-variable linear equation, where y is the dependent variable, x is th
independent variable, a (the intercept; value of y when x =0) and b (the slope; how big a
change in y we get for a 1-unit increase in x) are constants
What Does a Linear Equation Look Like with More Than Two Variables?
You can get better predictions of the criterion variable and your overall study if you base
them on more than one piece of information or predictor
You want to be able to look at the effect of one variable while controlling for other
variables accomplished by putting the other variables in the regression equation
Y = a +b1x1 + b2x2 general way of writing an equation with two independent
variables represented on a 3-D graph, and the equation would be represented by a
plane rather than a line
Why Does Multiple Regression Use Linear Equations?
A linear equation is the simplest way to describe a relationship between two or more
variables and still get reasonably accurate predictions
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