Linear Regression: estimation and hypothesis testing

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Linear Regression estimation and hypothesis
testing

• Hansel Burley

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Key terms

• Y-hatbXa regression equation
• Error
• Conditional distribution
• Standard error of the estimate
• Homoscedasticity
• Standard error of the regression coefficient

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Related topics

• Correlation is related to regression
• Bivariate distribution
• Scatterplot
• Estimating scores on Y based on scores on X
• Slope
• Constant
• Assumptions
• Normal with mean of predicted score
• Standard error of the estimate
• homoscedasticity

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• The conditional distribution is used to determine
  the percentage of Y values associated with a
  specific value of X
• CI95 is a range of scores for which the
  confidence is 95 percent that the interval will
  include the actual Y score

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Significance and Regression Coefficient

• When r 0, the regression coefficient 0
• No relationship, no prediction
• Important question How different from zero the
  regression coefficient must be in order to
  statistically enhance the prediction of Y scores
• Ans test the regression coefficient

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Topic Three

• Details about this topic
• Supporting information and examples
• How it relates to your audience

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Testing the regression coefficient

• 1. State the hypothesis
• Beta0
• 2. Set the criterion for rejecting the
  hypothesis
• T with n-2 df
• Mean is 0
• Standard error of the regression coefficient
• Std.err of est./square root of the sum of squares
  of the predictor

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• 3. Compute the test statistic
• 4. Interpret the results If significant, the
  regression coefficient is different from zero
  knowledge of one score (X) enhances knowledge of
  the other (Y)

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Next Steps

• Summarize any actions required of your audience
• Summarize any follow up action items required of
  you