1 1 2 2 k n r k r f rejection region f fk n k1 using

  • No School
  • AA 1
  • kjureb
  • 9

This preview shows page 5 - 7 out of 9 pages.

1 / 1 2 2 k n R k R F Rejection Region: F > F(k, n-(k+1) Using the p-value approach: Reject H 0 if p value < α where the p value = P(F(k, n (k+1)) > F) Conditions: 1) The error component ε is normally distributed. 2) The mean of ε is zero. 3) The variance of ε is σ 2 , a constant for all values of x. 4) The errors associated with different observations are independent. Multiple Regression Analysis Inference in Multiple Regression Testing the Utility of a Multiple Regression Model: The Global F Test Ho: β 1 = β 2 = … = β k = 0 Ha: At least one of the β parameter is nonzero. 1 / 1 2 2 k n R k R F Rejection Region: F > F(k, n-(k+1) Using the p-value approach: Reject H 0 if p value < α where the p value = P(F(k, n (k+1)) > F) Conditions: 1) The error component ε is normally distributed. 2) The mean of ε is zero. 3) The variance of ε is σ 2 , a constant for all values of x. 4) The errors associated with different observations are independent. Multiple Regression Analysis Testing the Utility of a Multiple Regression Model: The Global F Test Example : For the electrical usage example, Ho: β 1 = β 2 = … = β k = 0 Ha: At least one of the β parameter is nonzero. n = 10, k = 2 gives n (k+1) = 7 degrees of freedom. At α = 0.05, we reject Ho: β 1 = β 2 = 0 if F 0.05 (2,7) = 4.74 From the computer printout, computed F = 53.88. Since computed F > 4.74, we conclude that at least one of the model coefficient β 1 and β 2 is nonzero. 1 / 1 2 2 k n R k R F Multiple Regression Analysis Estimating and Testing Hypotheses about Individual Parameters The hypothesis for making inferences about particular β parameters is as follows: Ho: β j = 0 (j = 1, 2, … k) H 1 : β j > 0 Test Statistics: Degrees of freedom: (n [k + 1]) Rejection Region: t > t α (n [k+1]) ^ ^ j s t Multiple Regression Analysis Test of an Individual Coefficient in the Multiple Regression Model The hypothesis for making inferences about particular β parameters is as follows: a) Right-tailed test Ho: β j = 0 (j = 1, 2, … k) H 1 : β j > 0 Test Statistics: Degrees of freedom: (n [k + 1]) Rejection Region: t > t α (n [k+1]) ^ ^ j s t
Image of page 5