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Final

# STAT1008 Study Guide - Final Guide: Dependent And Independent Variables, Test Statistic, Confounding

Department
Statistics
Course Code
STAT1008
Professor
Bronwyn
Study Guide
Final

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Multiple Regression
Response variable: Y (quantitative)
k predictors: X1, X2, … Xk (quantitative or 0/1 categories)
Model: Y = β0 1X1 2X2 +···kXk
ε ~ N0,σε) and independent.
What to do?
Estimate the coefficients: b0, b1,…, k (estimate the same way as a simple model).
Test the individual predictors: t-tests (use ŷ?.
Assess the overall fit: R2, ANOVA.
T-tests for Individual Predictors:
Y = β0 1X1 +β2X2 +···+βkXk
Testing whether X2 be included in the model or not, eg: should exam 2 be in the model
given the presence of exam 1.
i.e. Testing the effectiveness of any predictor, say Xi, in a multiple regression model.
H0: βi = 0 vs Ha: βi 0
Test statistic: t = bi/Sebi
We find a p-value using a t-distribution with n - k - 1 df, where k is the number of
predictors.
If we reject the null we see that the predictor is an effective contributor to this model.
Individual t-tests assess the importance of a predictor after the other predictors are
already in the model, eg: if I add another predictor into the model, exam 1 may
eoe isigifiat.
Assessing Overall Fit: R2
R2 = % of ariailit i Y hih is eplaied  the odel.
SSTotal =  (as for one predictor)
SSE =   (as for one predictor)
SSModel = SSTotal SSE
R2 = SSModel/SSTotal
R2 is interpreted as the percent of variability in the response values in the sample that
is explained by the fitted regression model.
Eg: If R2 =0.525, this means that 52.5% of the variability in Final exam scores is
explained by the model based on exam 1 and exam 2.
Assessing Overall Fit: ANOVA
To test for the overall effectiveness of a regression model: Y = β0 + β1X1 2X2 +···+βkXk
H0: βi = β2 =…= βk = 0 (the model is ineffective)
Ha: At least oe βi 0 (at least one predictor in the model is effective)
Mean square = SS/df
10.2 Checking Regression Conditions
Conditions for a Regression Model:
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