This preview shows pages 1–10. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: STAT 350 Lecture 23 Chapter 11 Inferential Methods in Regression and Correlation linear regression Simple Linear Regression: Fit a line in the data when you see a linear trend Minimizing the errors using LS method Get estimates of slope and intercept accordingly linear regression Sample Least Square Regression Line: Minimizes Random residuals Residuals: What is the sum of residuals? Population Least Square Regression Line Linear Regression model for population Statistical Inference based on random samples SS Re sid SSE y i y i 2 e i y i y i Simple Linear Regression Model The true regression line as a model: y i = + x i + e i In this model: e i is assumed to follow a normal distribution with mean 0 and standard deviation all e i s are assumed independent of each other Example Suppose the simple linear regression equation is given as y=5.000.01x+e with =0.075 1) What is the mean value of y when x=100? x=200? x=500? 2) What is the standard deviation of y when x=100? x=200? x=500? Example Suppose the simple linear regression equation is given as y=5.000.01x+e with =0.075 1) What is the mean value of y when x=100? x=200? x=500? Solution: when x=100, y=4+e. Since e has a normal distribution with mean 0, the mean value for y is 4. Similarly, when x=200, the mean value of y is 3; And when x=500, the mean value of y is 0. Example Suppose the simple linear regression equation is given as y=5.000.01x+e with =0.075 2) What is the standard deviation of y when x=100? x=200? x=500? Solution: When x=100, y=4+e. Since e has a normal distribution with =0.075, the standard deviation of y is also =0.075. Adding a constant term 4 does not change the standard deviation. In general, the standard deviation of y given any x value is =0.075. Estimating the slope and intercept A point estimate of is b A point estimate of is a b S xy S xx x i y i 1 n ( x i )( y i ) x i 2 1 n ( x i ) 2 a y bx Example 11.2 on page 494Example 11....
View
Full
Document
 Spring '08
 Staff
 Correlation, Linear Regression

Click to edit the document details