Lecture23

Lecture23 - STAT 350 Lecture 23 Chapter 11 Inferential...

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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=5.00-0.01x+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=5.00-0.01x+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=5.00-0.01x+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....
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Lecture23 - STAT 350 Lecture 23 Chapter 11 Inferential...

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