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Chapter 14 - Inference for Regression

Chapter 14 - Inference for Regression. Paul M. Wilson, Jr. May 29, 2002 AP Statistics. Introduction - Chapter 3 All Over Again!.

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Chapter 14 - Inference for Regression

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  1. Chapter 14 - Inference for Regression Paul M. Wilson, Jr. May 29, 2002 AP Statistics

  2. Introduction - Chapter 3 All Over Again! • We use the linear regression model when a scatterplot shows a linear relationship between a quantitative explanatory variable “x” and a quantitative response variable “y”.

  3. Do the following when given a set of data: • Make a scatterplot plotting the explanatory variable “x” horizontally and the response variable “y” vertically. • Use a calculator to fit the LSRL to the data. • Look for outliers and influential observations. • Calculate the correlation “r” and its square.

  4. Don’t forget the equation for the LSRL! The equation to calculate resids is still the same! We have a standard error about the LSRL. Degrees of freedom! We have a confidence interval for regression slope. There are also standard hypotheses for no linear relationship. Equations to Remember in Linear Regression

  5. The Equations for Regression Inference • Equations for the LSRL, residuals, and the standard error about the LSRL:

  6. Equations Continued • We also have equations for degrees of freedom and the confidence interval: • We use n-2 degrees of freedom since we have two variables to observe.

  7. The null hypothesis states that there is no linear relationship and is written in the form of: The alternative states that there is in fact some linear relationship and can be written in one of 3 forms: The Null and Alternative Hypotheses

  8. 3 Basic Assumptions for Regression • The true relationship is linear : look at the scatterplot to check that the overall pattern is roughly linear. • The standard deviation of the response about the true line is the same everywhere. • The response varies normally about the true regression line.

  9. Quick Facts about the Confidence Interval • We use a confidence interval to estimate the mean response. • A confidence interval says that the interval obtained is correct a certain percentage of the time in repeated use. • The confidence interval for the mean response “u” is

  10. More advanced work in linear regression can be found throughout Chapter14!

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