We want to test whether or not the addition of 3 variables to amodel will be statistically significant. You are given thefollowing information based on a sample of 25observations.
ŷ = 62.470 − 1.835x1 + 25.610x2
SSE = 785; SSR = 556
The model was also estimated including the 3 variables. Theresults are:
ŷ = 59.220 − 1.766x1 + 25.639x2 + 16.238x3 + 15.294x4 − 18.722x5
SSE = 580; SSR = 761
(a)
State the null and alternative hypotheses.
H0: 𝛽1 = 𝛽2 = 𝛽3 = 𝛽4 = 𝛽5 =0Ha: One or more of the parameters is not equalto zero.H0: One or more of the parameters isnot equal to zero.Ha: 𝛽3 = 𝛽4 = 𝛽5 H0: 𝛽3 = 𝛽4 = 𝛽5 =0Ha: One or more of the parameters is not equalto zero.H0: One or more of the parameters isnot equal to zero.Ha: 𝛽1 = 𝛽2 = 𝛽3 = 𝛽4 = 𝛽5 =0
(b)
Test the null hypothesis at the 5% level of significance.
Find the value of the test statistic. (Round your answer to twodecimal places.)
Find the p-value. (Round your answer to threedecimal places.)
p-value =
Is the addition of the three independent variablessignificant?
Do not reject H0. We conclude that theaddition of the three independent variables is not statisticallysignificant.Reject H0. We conclude thatthe addition of the three independent variables is statisticallysignificant. Reject H0.We conclude that the addition of the three independent variables isnot statistically significant.Do notreject H0. We conclude that the additionof the three independent variables is statisticallysignificant.
We Want To Test Whether Or Not The Addition Of 3 Variables To A Model Will Be Statistically Significant You Are Given T 1 (102.89 KiB) Viewed 12 times
We want to test whether or not the addition of 3 variables to a model will be statistically significant. You are given the following information based on a sample of 25 observations. ŷ= 62.4701.835x₁ + 25.610x₂ SSE 785; SSR 556 The model was also estimated including the 3 variables. The results are: y = 59.220 - 1.766x₁ + 25.639x₂ + 16.238x3+15.294x4 - 18.722x5 SSE 580; SSR = 761 (a) State the null and alternative hypotheses. Ho: B₁ = B₂ = B3 = P4=B5 = 0 Ha: One or more of the parameters is not equal to zero. O Ho: One or more of the parameters is not equal to zero. Ha: B3 = P4=B5 Ho: B3 B4 = B5 = 0 H₂: One or more of the parameters is not equal to zero. O Ho: One or more of the parameters is not equal to zero. Ha: P₁ P₂ P3 P4 P5 = 0 (b) Test the null hypothesis at the 5% level of significance. Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = Is the addition of the three independent variables significant? O Do not reject Ho. We conclude that the addition of the three independent variables is not statistically significant. O Reject Ho. We conclude that the addition of the three independent variables is statistically significant. O Reject Ho. We conclude that the addition of the three independent variables is not statistically significant. O Do not reject Ho. We conclude that the addition of the three independent variables is statistically significant.
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