Question

Zambia is import-dependent country shows import model is given as Y= β"0"+ β"1" X"1"+β"2" X"2"+ μ where Y is total imports, X1 is GNP and X2 is price Index of imports. For the past twelve months, data has been collected and compiled as in the table below

Obs	1	2	3	4	5	6	7	8	9	10	11	12
Y	57	43	73	37	64	48	56	50	39	43	69	60
X1	220	215	250	241	305	258	354	321	370	375	385	385
X2	125	147	118	160	128	149	145	150	140	115	155	152

REQUIRED

a). Estimated model and interpret the results (18mks)

b). Compute the unexplained variations of the model (3Mks)

c). Determine the overall significance of the Model (4mks) (Hint: Use ANOVA/F test)

Answer 1

here I have used Excel and solve it: DATA> Data Analysis > chose regression >y range as y>x range as x1 and x2 all observation (1 to 12) SUMMARY OUTPUT a)estimated regression model is Regression Statistics ANOVA yhat-bo+(b1*x1)+(b2*x2) Multiple 0.296469 MS gnificance F R Square 0.087894 Regressio 2 135.0271 67.51355 0.433637 0.661004 bo Adiusted -0.1148 Residual 75.40513 9 1401.223 155.6914 b1 Standard 12.47764 Total 0.025365 11 1536.25 b2 0.21329 Observati 12 yhat 75.40513 (0.025365 x1)+(-0.21329*x2) Coefficientandard Err P-value Lower 95%Upper 95%ower 95.09 pper 95.0% t Stat Intercept75.40513 37.981771.985298 0.078388-10.5156 161.3259-10.5156 161.3259 yhat is estimated regression model 0.025365 0.056462 0.449249 0.663875-0.10236 0.153091-0.10236 0.153091 0.21329 0.25046 -0.85159 0.416524 -0.77987 0.353291 -0.77987 0.353291 here test for x1 coefficient: use p value approach here p value is 0.663875 p value is greater than alpha value hence coefficient of x1 is not significant.

here test for x2 coefficient: use p value approach here p value is 0.416524 p value is greater than alpha value hence coefficient of x2 is not significant. here both x1 and x2 is not significant at alpha value. unexplained variation 1- R square value here R square value is 0.087894 0.912106 which is too large varition unexplained by model is 91.2106 percent. ##c) overall significance of the model is not significant use p value approach here p value is 0.661004 because it p value is greater than not significant. That is model is not significant. alpha value hence it is