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) 12/5/2018 ST3131, Lecture 5

Review of Lecture 4 Interpretation of CI? 12/5/2018 ST3131, Lecture 5

Prediction: for SLR Model Standard Errors 12/5/2018 ST3131, Lecture 5

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 12/5/2018 ST3131, Lecture 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. 12/5/2018 ST3131, Lecture 5

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: 12/5/2018 ST3131, Lecture 5

D. Properties of the estimator: C. Solution: Properties: D. Properties of the estimator: (1). Linearity (4). Best Linear Unbiased Estimator 12/5/2018 ST3131, Lecture 5

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

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: 12/5/2018 ST3131, Lecture 5

D. Properties of the estimator: C. Solution: D. Properties of the estimator: (1). Linearity (4). Best Linear Unbiased Estimator 12/5/2018 ST3131, Lecture 5

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

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: 12/5/2018 ST3131, Lecture 5

C. Paired two-sample t-test Trivial Model against No-slope Model C. Paired two-sample t-test 12/5/2018 ST3131, Lecture 5

The two-sample t-test becomes one-sample t-test: Transformation: The two-sample t-test becomes one-sample t-test: 12/5/2018 ST3131, Lecture 5

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