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8.4 Hypothesis Testing For GLM

  1. Simple linear regression
    1. If the p-value for the model is less than alpha, then it is believed the single independent variable is helpful in predicting/understanding the dependent variable.
    2. If the p-value for the model is greater than alpha, then it is believed the single independent variable is not helpful in predicting/understanding the dependent variable and that β1 = 0.
  2. Multiple linear regression
    1. If the p-value for the model is less than alpha then it is believed at least some of the independent variables are helpful in predicting/understanding the dependent variable.
    2. If the p-value for the individual independent variable is less than alpha this implies that the particular independent variable is helpful in predicting/understanding the dependent variable.
    3. if the p-value for the independent variable, xi, is greater than or equal to alpha it is believed that βi = 0, and thus the independent variable can be removed from the model.
  3. General linear model
    1. If the p-value for the model is less than alpha then it is believed that at least some of the independent variables are helpful in predicting/understanding the dependent variable.
    2. If the p-value for the individual independent continuous variable is less than alpha this implies that the particular independent variable is helpful in predicting/understanding the dependent variable.
    3. If the p-value for the individual independent categorical variable is less than alpha this implies that the particular independent variable is helpful in predicting/understanding the dependent variable.
      • If some categories of a categorical variable are significant (p-value less than alpha) but others are not, use the categorical variable as it is.
        • Handling this situation in a better manner goes beyond the scope of this text.
    4. If the p-value for the independent variable, xi, is greater than or equal to alpha it is believed that βi = 0, and thus the independent variable can be removed from the model.

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