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  • An F-test explains how well the dependent variable is explained by the independent variables collectively
  • In case of multiple independent variable, F-test tells us whether a single variable explains a significant part of the variation in dependent variable or all the independent variables explain the variability collectively
  • Suppose Edward now wants to check whether the household income and expenses collectively explains the variation in his pocket money
  • The following hypothesis can be formed:
  • H0: HI=HE=0 versus Ha: At least HI or HE ≠ 0
  • F-statistic is given as:
  • Where:
    • MSR: Mean Regression sum of squares
    • MSE: Mean Squared Error
    • n: Number of observations
    • k: Number of independent variables
  • Decision rule for F-test:  Reject H0 if the F-statistic > Fc (Critical Value)
  • The numerator of F-statistic has degrees of freedom of "k" and the denominator has the degrees of freedom of "n-k-1"
  • If H0 is rejected then at least one out of two independent variable is significantly different that zero.
  • This implies that at least one out of household income(independent variable) or household expenses(independent variable) explains the variation in the pocket money of Edward


F-test is always a single tailed test while testing the hypothesis that the coefficients are simultaneously equal to zero


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