ECON209O0Y 4. Regression analysis was individually applied between with 202 obse
ID: 3332735 • Letter: E
Question
ECON209O0Y 4. Regression analysis was individually applied between with 202 observations Model 1 100+10 X Model Model 3 the dependent variable Y and three varables X, Xs and Xs. The folowing estimated regression eau equations were Su 30 Sea = 20 Ses 10 Ra 70 2100+30 X 100-30 x For a level of significance of 5%; a) Which variable can explain individually and statistically better the behaviour of Y? b) Could the F test be useful in this case? c)Can you predict the value ory when A+ 10n«10 and X-10using any of the previous Models 1, 2 or 37 Regression analysis was also applied between the dependent variable Y and two independent variables altogether Xo and Xa. The following estimated regression equation was obtained with 43 observations Model 4 100+50 xs-60 x So410 SSR 90 SSE-10 For a level of significance of 1%: d) Could the F test be useful in this case? e) Can you predict the value of Y when X1 -10, X2-10, X3 10 and X 10? 30 poinExplanation / Answer
4. a From the values of R^2 (which measures proportion of variation in y explained by x), model1 seem to explain individually (R^2=0.70) better behaviour of Y. That is 70% variability in Y is accounted for variation in X. The corresponding t test statistic, t=coefficient/SE(coefficient)=10/30=0.33, p value: 0.7970, p value not less than 0.05, therefore, there is insufficient sample evidence to conclude that x is useful for predicting y. Similarly, model B also has p value for t test greater than 0.05, and model C too has p value for t test greater than 0.05. Thus, neither of the model can explain better behaviour of Y.
b. Since, it has been determined that x is not useful for predicting y, therefore, F test is not suitable.
c. It is not known whether the given values for x has either been used to calculate the regression equation or falls within the range of values of x for determining regression equation. Thus, they cannot be used to predict y. Moreover, it has alreday been proved that x is not useful in prediting y.
d.
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