Very Hard, tough question

An analyst covering the banking sector is given the data in Table 1 and is asked to construct a model explaining the relationship between the GDP growth rate and the percentage of non-performing loan in BBB bank's loanbook. Regression estimates is given in Table 2.Table 1: DataYear X=GDP... 顯示更多 An analyst covering the banking sector is given the data in Table 1 and is asked to construct a model explaining the relationship between the GDP growth rate and the percentage of non-performing loan in BBB bank's loan book. Regression estimates is given in Table 2. Table 1: Data Year X=GDP growth Y=% of non-performing loan 2000 5% 0.02 2001 1% 0.3 2002 - 2% 1.2 2003 -3% 2 2004 5% 0.5 Table 2: Regression Output Predictor Coefficient Standard Error of the Coefficient Intercept 0.010221 0.002246 Slope -0.18176 0.06279 Question: 1) t-statistic of the correlation coefficient? Can we conclude, with 95% confidence is significantly different from zero? 2) t-statistic of the intercept? Can we conclude, with 95% confidence, that the intercept is significantly different from zero? 3) t-statistic of the slope? Can we conclude, with 95% confidence, that the slope is significantly different from zero?

Note that Σx = 0.06, Σx2 = 0.006 4 Σy = 0.040 2, Σy2 = 0.000 578 04 Σxy = -0.000 55. So SSX = 0.0064 - 0.062/5 = 0.005 68, SSXY = -0.00055 - 0.06 * 0.0402/5 = -0.001 032 4, SSY = 0.000578 - 0.04022/5 = 0.000 254 832 (1) H0: Population correlation coefficient = 0. H1: Population correlation coefficient ≠ 0. Correlation coefficient r = SSXY/√(SSX * SSY) = -0.858 12. t-statistic = r/√[(1 - r2)/(n-2)] = -2.895. Using 0.05 level of significance with d.f. = 3, t3 = 3.1824. Since t > -t3, we do not reject the null hypothesis H0. Hence there is NO EVIDENCE that the correlation coefficient is significant different from zero. (2) H0: Actual intercept = 0. H1: Actual intercept ≠ 0. Estimated intercept b = 0.010 221. Standard error Sb = 0.002 246. t-statistic = b/(Sb/√n) = 10.176. Using 0.05 level of significance with d.f. = 4, t4 = 2.7764. Since t > t4, we reject the null hypothesis H0. Hence there is EVIDENCE that the intercept is significant different from zero. (3) H0: Actual slope = 0. H1: Actual slope ≠ 0. Estimated slope m = -0.181 76. Standard error Sm = 0.062 79. t-statistic = m/(Sm/√n) = -0.647 28. Using 0.05 level of significance with d.f. = 4, t4 = 2.7764. Since t > -t4, we do not reject the null hypothesis H0. Hence there is NO EVIDENCE that the slope is significant different from zero.

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