{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Chapter 05

# Chapter 05 - Chapter 5 Regression Essential Statistics...

This preview shows pages 1–7. Sign up to view the full content.

Essential Statistics Chapter 5 1 Chapter 5 Regression

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

View Full Document
Essential Statistics Chapter 5 2 Objective : To quantify the linear relationship between an explanatory variable (x) and response variable (y). We can then predict the average response for all subjects with a given value of the explanatory variable. Linear Regression
Essential Statistics Chapter 5 3 Prediction via Regression Line Number of new birds and Percent returning Example : predicting number (y) of new adult birds that join the colony based on the percent (x) of adult birds that return to the colony from the previous year.

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

View Full Document
Essential Statistics Chapter 5 4 Least Squares Used to determine the “best” line We want the line to be as close as possible to the data points in the vertical ( y ) direction (since that is what we are trying to predict) Least Squares : use the line that minimizes the sum of the squares of the vertical distances of the data points from the line
Essential Statistics Chapter 5 5 Least Squares Regression Line Regression equation: y = a + bx ^ x is the value of the explanatory variable y-hat is the average value of the response variable (predicted response for a value of x) note that a and b are just the intercept and slope of a straight line note that r and b are not the same thing, but their signs will agree

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

View Full Document
Chapter 5 6 Prediction via Regression Line Number of new birds and Percent returning The regression equation is y-hat = 31.9343 - 0.3040 x y-hat is the average number of new birds for all colonies with percent x returning For all colonies with 60% returning, we predict the average number of new birds to be 13.69: 31.9343 - (0.3040)( 60 ) = 13.69 birds Suppose we know that an individual colony has
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 24

Chapter 05 - Chapter 5 Regression Essential Statistics...

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online