1. Review of Chapter 3 where Multiple Linear Regression Model:
LS Estimators
where
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ST3131, Review of chapter 3

2. Noise variance estimator:
Fitted values:
Residuals:
Noise variance estimator:
Decompositions
Observation
Squares
SST = SSR SSE
Degrees of Freedom
df(SST) = df(SSR) df(SSE)
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ST3131, Review of chapter 3

3. Interpretation of the Coefficients
Another Interpretation:
Assumption:
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ST3131, Review of chapter 3

4. 3). BLUE estimators (Best Linear Unbiased Estimators)
Properties:
1). Linearity
2). Unbiased
3). BLUE estimators (Best Linear Unbiased Estimators)
4) Normality
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ST3131, Review of chapter 3

5. Variances of the Estimates
Noise variance estimator and Standard Errors
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ST3131, Review of chapter 3

6. Inferences for Individual Coefficients/T-test
Hypothesis Testing
Confidence Interval
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ST3131, Review of chapter 3

7. Steps for Model Comparison/F-test :
RM H0: The RM is adequate vs FM H1: The FM is adequate
Step1: Fit the FM and get SSE (in the ANOVA table)
df (in the ANOVA table)
R_sq (under the Coefficient Table)
Step 2: Fit the RM and get SSE, df, and R_sq.
Step 3: Compute F-statistic:
Step 4: Conclusion: Reject H0 if F>F(r,df(SSE,F),alpha)
Can’t Reject H0 otherwise.
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ST3131, Review of chapter 3

8. Special Case: ANOVA Table (Analysis of Variance)
Source
Sum of Squares df
Mean Square
F-test
P-value
Regression
SSR p
MSR=SSR/p
F=MSR/MSE
Residuals
SSE
n-p-1
MSE=SSE/(n-p-1)
Total
SST
n-1
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ST3131, Review of chapter 3

9. Coefficient Table
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ST3131, Review of chapter 3

10. Multiple Correlation Coefficients
R-square measures the percentage of the total variability in Y
Explained by the MLR.
11/21/2018
ST3131, Review of chapter 3