1. OUTLINE Lecture 5 A. Review of Lecture 4 B. Special SLR Models
1. No Intercept Model
2. No Slope Model
3. Trivial Model (No Intercept and No Slope)
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ST3131, Lecture 5

2. Review of Lecture 4
Interpretation of CI?
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ST3131, Lecture 5

3. Prediction: for SLR Model
Standard Errors
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4. Method 4: Use Hypothesis Test
Methods for Assessing the Linear Relationship/Quality of Linear Fit
Method 1: Use the Correlation Cor(X,Y)
Method 4: Use Hypothesis Test
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ST3131, Lecture 5

5. To find the estimates for Special SLR models
General SLR Model :
No Intercept Model :
No Slope Model :
Trivial Model :
AIMs:
To find the estimates for Special SLR models
2. To study the statistical inferences, e.g.,HT, CI, and PI etc.
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ST3131, Lecture 5

6. A. Cases when we use no-intercept models:
From prior knowledge (subject matters/external considerations)
e.g., physics/economic principles.
2. From formal hypothesis test, e.g., the intercept is not significant.
B. Estimation:
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7. D. Properties of the estimator:
C. Solution:
Properties:
D. Properties of the estimator:
(1). Linearity
(4). Best Linear Unbiased Estimator
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ST3131, Lecture 5

8. Remark: E. Hypothesis Tests F. Confidence Interval 12/5/2018
ST3131, Lecture 5

9. A. Cases when we use no-slope models:
No predictor variables are of interest
2. Data are assumed from an underlying sample
3. From formal hypothesis test, e.g., “the slope is not significant”
is not rejected.
B. Estimation:
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ST3131, Lecture 5

10. D. Properties of the estimator:
C. Solution:
D. Properties of the estimator:
(1). Linearity
(4). Best Linear Unbiased Estimator
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ST3131, Lecture 5

11. E. Hypothesis Tests
F. Confidence Interval
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ST3131, Lecture 5

12. Trivial Regression Model
A. Cases when we use trivial regression models:
1. Data are known to be pure noise
2. From formal hypothesis test, e.g. “both slope and intercept
Are not 0” is not rejected.
3. Trivial model and no-slope model are related to one-sample
T-test and paired two-sample t-test.
B. One-sample t-test:
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ST3131, Lecture 5

13. C. Paired two-sample t-test
Trivial Model against No-slope Model
C. Paired two-sample t-test
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14. The two-sample t-test becomes one-sample t-test:
Transformation:
The two-sample t-test becomes one-sample t-test:
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ST3131, Lecture 5

15. 1. In what cases, we will use special simple linear regression models?
Questions:
1. In what cases, we will use special simple linear regression models?
2. Draw a data set which suggests that we can use a no-intercept simple linear model.
3. Draw a data set which suggests that we have to use a general simple linear regression model.
12/5/2018
ST3131, Lecture 5