Quantitative Business Analysis for Decision Making. Multiple Linear Regression Analysis. Outlines. Multiple Regression Model Estimation Testing Significance of Predictors Multicollinearity Selection of Predictors Diagnostic Plots. Multiple Regression Model.
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Multiple linear regression model:
are slope coefficients of
X1, X2 ,… ,Xk.
quantifies the amount of change in
response Y for a unit change in Xi when
all other predictors are held fixed.
In the model,
is the mean of Y.
A random sample of n units is taken. Then for
each unit k+1 measurements are made:
Y, X1 , X2 , …., Xk
Estimated multiple regression model is:
Expressions for bi are cumbersome to
write. is an estimate of
Sample standard deviation around the mean (estimated regression model) is:
It is an estimate of
Standard error of (for specified values of predictors) is denoted by
For comparing with a reference ,test
and for estimating by a confidence
Coefficient of determination R2 quantifies the % of
variation in the Y-distribution that is accounted by the
predictors in the model. If
Null hypothesis = predictors in the relationship have no predictive power to explain the variation in Y-distribution
Test statistic: F = . It has
F- distribution with k and (n-k-1) degrees of
freedoms for the numerator and denominator.
correlated among themselves. In its presence R2 may be high,
but individual coefficients are less reliable.
multicollinearity by selecting only those predictors that are not
strongly correlated among themselves.
variability, and need for transformation to achieve
numerical codes that are used to represent qualitative