Simple Linear Regression Model and Parameter Estimation

Simple Linear Regression Model and Parameter Estimation

Reading: Section 12.1 and 12.2 Learning Objectives: Students should be able to: ? Understand the assumptions of a regression model ? Correctly interpret the parameters of a regression model ? Estimate the parameters of a regression model

1

Simple Regression Analysis

? Regression analysis deals with investigation of the nondeterministic relationship between two (or more) variables.

? Simple linear regression model: non-deterministic linear relationship between two variables.

2

Fixed Predictor and Random Response Variable

? For a fixed value of x, the value of Y is random, varying around a "mean value" determined by x.

? x variable: independent / predictor / explanatory variable ? Y variable: dependent / response variable

3

Scatter Plot - Checking Linear Relationship

Example: Relationship between diesel oil consumption rates measured by two methods

Pairwise data (x1,y1), (x2, y2), ..., (xn, yn)

x y x- rate measured by drain-weigh method

4 5

5 7

Y-rate measured by CI-trace method

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17 13

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22 20

28 24

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31 28

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Simple Linear Regression Model & Interpretation

Regression model

Regression line

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