emember to show your work, Use the rejection region method for all hypotheses te
ID: 3045899 • Letter: E
Question
emember to show your work, Use the rejection region method for all hypotheses test questions. Use a 5 percent significance level unless otherwise stated. Note: R Question 1 Consider the following model WACL to expenditure TOTEXP, age of the household head AGE, and the number of children in the that relates to the proportion of a household's budget spent on alcohol household NK WALC-B. + |n (TOTEXP) + 9AGE + .NK + Relevant data were used to estimate this model. Note that only households with one or two children are being considered. Thus, NK takes only the values one or two. Output from estimating this appears in the table below Dependent Variable: WALC Included observation: 1519 Variable t-Statistic Std. Error 0.0190 Prob. 0.6347 0.0000 0.0000 0.0000 0.0606 0.0633 0.0091 0.0276 In(TOTEXP AGE NK R-squared S.E of the estimate Error sum of squares 6.6086 -6.9624 4.0303 Mean dependent var 0.0002 -0.0133 0.0033 S.D. dependent var 5.752896 a. Fill in the following blank spaces that appear in this table. (i) The t-statistic for b () The standard error of b (n) The coefficient estimate b (iv) R (v) The standard error of the estimate, Se b. Interpret the coefficient estimate for the AGE variable c. Conduct the F-test for the model. Does this test indicate a good fit of the model? Explain clearlyExplanation / Answer
(a) t-statistic for coefficient=coefficient/SE(coefficient)
(i)t(b1)=b1/SE(b1)=0.0091/0.0190=0.4789
(ii)SE(b2)=b2/t(b2)=0.0276/6.6086=0.0042
(iii)b3=t(b3)*SE(b3)=-6.9624*0.0002=0.0014
(iv) SD(y)=0.0633, var(y)=0.0633*0.0633=0.0040
Total sum of square=0.0633*0.0633*1519=6.60865
R2=1-error SS/Total SS=1-5.752896/6.60865=0.12949
(v) MSE=Error SS/ Error df=ErorrSS/(n-p)=5.75286/(1519-4)=0.003797
Se=sqrt(MSE)=sqrt(0.003797)=0.0616198
(c)
since model F is more than critical F at 1% level of signiciance, so we can say tha model is good fit
(b) impact of Age is significant negative on dependent variable at 1% level of significane as its p-value is less than alpha=0.01
(c)
SS df MS F Critical F(0.01) Model 0.855754 3 0.285251 75.02052 3.794577981 Error 5.752896 1513 0.003802 Total 6.60865 1516Related Questions
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