Consider a portion of simple linear regression results, y = 104.35 + 27.50x_1: S

Question

Consider a portion of simple linear regression results, y = 104.35 + 27.50x_1: SSE = 407 281; n = 30 In an attempt to improve the results, two explanatory variables are added. A portion of the regression results are y = 4.57 + 17.62x_1 - 27.65x_2 + 6.63x_3; SSE = 339, 526; n = 30. Use Table 4. a. Formulate the hypotheses to determine whether x_2 and x_3 are jointly significant in explaining y. H_0: beta_2 = beta_3 = 0; H_A: At least one of the coefficients is nonzero. H_0: beta_1 = beta_2 = beta_3 = 0; H_A: At least one of the coefficients is nonzero. H_0: beta_2 = beta_3 = 0; H_A: At least one of the coefficients is greater than zero. b. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) Test statistic c. At the 10% significance level, find the critical value. Critical value

Explanation / Answer

a) The hypothesis whether x2 and x3 are jointly significant in explaining y

                          H0 : 1 = 2= 3 ; HA : At least one of the coefficient is non zero

                          2nd option is correct

b) n=30 ,

k= no. of independent variable =3

q =no. of variables tested to b =2

Test statistic F=[ (SSER –SSEUR)/q] / [(SSEUR /(n-k-1))]

                        =[(407281-339526)/2] / [(339526/(30-3-1)]

                        =33877.5 / 13058.6923

                        =2.5942

              F =2.59

c) Critical value at 10% significance level

              F-critical =F0.1,2,26 =2.5191

              F-critical =2.52

F-critical (2.52) < F(2.59) reject H0

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