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Chapter 14 - Inference for Regression

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Title: Chapter 14 - Inference for Regression


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
Equations to Remember in Linear Regression
  • Dont 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.

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 and Alternative Hypotheses
  • 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

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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