notes Ch 12

notes Ch 12 - CHAPTER 12 Simple Linear Regression 12.1...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: CHAPTER 12 Simple Linear Regression 12.1 Model The regression model used in simple linear regression is: + + = x y 1 and 1 are the parameters of the model and (epsilon) is a random number variable referred to as the error term. The equation that describes how the expected value of y, denoted E(y), is related to x is called the regression equation. x y E 1 ) ( + = The parameters and 1 are typically unknown. Sample statistics (denoted b and b 1 ) are computed as estimates of the population parameters and 1 . The estimated simple linear regression equation is a line given by x b b y 1 ^ + = Where b is the y-intercept and 1 b is the slope. 12.2 Least Squares Method The least squares method is a procedure for using sample data to find the estimated regression equation. Case: The student population and quarterly sales data for 10 Armands Pizza Parlors are provided in the table below. Restaurant Student Population [1000s] Quarterly Sales [$1000s] i x i y i 1 2 58 2 6 105 3 8 88 4 8 118 5 12 117 6 16 137 7 20 157 8 20 169 9 22 149 10 26 202 1 Based on the data, a scatter diagram of the student population and quarterly sales can be created. Scatter Diagram 50 100 150 200 250 5 10 15 20 25 30 Student Population [1000s] Quarterly Sales [$1000s The diagram shows a positive relationship between the student population and quarterly sales. The least squares criterion is min 2 ^ ) ( - y y i where i y = observed value of the dependent variable for the ith observation and y = estimated value of the dependent variable for the ith observation Differential calculus can be used to show that values of b and 1 b that minimize the above expression can be found by using the following two equations: x b y b x x y y x x b i i i 1 2 1 ) ( ) )( (- =--- = Where i x = value of the independent variable for the ith observation i y = value of the dependent variable for the ith observation x = mean value for the independent variable y = mean value for the dependent variable n = total number of observations...
View Full Document

Page1 / 8

notes Ch 12 - CHAPTER 12 Simple Linear Regression 12.1...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online