Chapter 14 - Inference for Regression

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Chapter 14 - Inference for Regression

• Paul M. Wilson, Jr.
• May 29, 2002
• AP Statistics

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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.

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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.

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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.

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The Equations for Regression Inference

• Equations for the LSRL, residuals, and the
  standard error about the LSRL

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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.

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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

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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.

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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

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