STAT1008 Lecture Notes - Lecture 35: Dependent And Independent Variables, Tachykinin Receptor 1, Standard Deviation

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30 May 2018
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STAT1008 Week 12 Lecture B
T-test for individual predictors
Y = Beta0 + beta1x1 + beta2x2 + … + betakxk + epsilon
H0: bi = 0
Ha: bi doesn’t = 0
T = bi/SE where bi is from the p-value from tn-k-1 and SE and T is given in output
Exam 1 has the lowest p-value
Predicting Final Exam:
Exam 2: 0.215086 thus have not enough evidence to reject your null
Individual t-tests assess the importance of a predictor after the other predictors
are already in the model
If i add other predictors into the model exam 1 may become “insignificant”
Assessing overall fit: R2
R2 = % of variability in Y which is “explained” by the model
SSTotal = sum of (y-ybar)2 (as for one predictor)
SSE = sum of (y-yhat)2 (as for one predictor)
SSModel = SSTotal - SSE
R2 = SSModel/SSTotal
Adding Exam 2 in the example increases R2
Final grade models:
Two predictor model:
52.5% of the variability in Final exam scores is explained by the model
based on Exam 1 and Exam 2
Four predictor model:
59.4% of the variability in Final exam scores is explained by the model
based on Exam 1, Exam 2, QuizAvg and projects
Adding new predictors to a model increases R2, but is the increase worth it?
Assessing Overall fit: ANOVA
Y = Beta0 + beta1x1 + beta2x2 + … + betakxk + epsilon
H0: beta1 = beta2 = … = betak = 0 (model is ineffective)
Ha: some betai doesn’t = 0 (model is effective)
Total variability in Y (sum of y-ybar)2 = variability explained by model (sum of
yhat - ybar)2 + unexplained variability in error (sum of y-yhat)2
ANOVA for multiple regression
H0: beta1 = beta2 = … betak = 0 (model is ineffective)
Ha,: Some betai doesn’t = 0 (model is effective)
Source
d.f.
Sum of
Mean
F-statistic
P-value
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Document Summary

T = bi/se where bi is from the p-value from tn-k-1 and se and t is given in output. Exam 2: 0. 215086 thus have not enough evidence to reject your null. Individual t-tests assess the importance of a predictor after the other predictors are already in the model. If i add other predictors into the model exam 1 may become insignificant . R2 = % of variability in y which is explained by the model. Sstotal = sum of (y-ybar)2 (as for one predictor) Sse = sum of (y-yhat)2 (as for one predictor) Adding exam 2 in the example increases r2. 52. 5% of the variability in final exam scores is explained by the model based on exam 1 and exam 2. 59. 4% of the variability in final exam scores is explained by the model based on exam 1, exam 2, quizavg and projects. Y = beta0 + beta1x1 + beta2x2 + + betakxk + epsilon.

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