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# Consider the following regression modelYiÃ¢â‚¬â€ž=Ã¢â‚¬â€žÃŽÂ²0Ã¢â‚¬â€¦+Ã¢â‚¬â€¦ÃŽÂ²1X1iÃ¢â‚¬â€¦+Ã¢â‚¬â€¦ÃŽÂ²2X2iÃ¢â‚¬â€¦+Ã¢â‚¬â€¦ÃŽÂ²3X3iÃ¢â‚¬â€¦+Ã¢â‚¬â€¦ÃŽÂ²4X4iÃ...

## Question

###### Consider the following regression modelYiÃ¢â‚¬â€ž=Ã¢â‚¬â€žÃŽÂ²0Ã¢â‚¬â€¦+Ã¢â‚¬â€¦ÃŽÂ²1X1iÃ¢â‚¬â€¦+Ã¢â‚¬â€¦ÃŽÂ²2X2iÃ¢â‚¬â€¦+Ã¢â‚¬â€¦ÃŽÂ²3X3iÃ¢â‚¬â€¦+Ã¢â‚¬â€¦ÃŽÂ²4X4iÃ¢â‚¬â€¦+Ã¢â‚¬â€¦ÃŽÂ²5X5iÃ¢â‚¬â€¦+Ã¢â‚¬â€¦uiThis model has been estimated by OLS. The Gretl output isbelow.Model 1: OLS, using observations 1-56coefficientstd. errort-ratiop-valueconst-0.38590.5198-0.74240.4613X10.30650.20781.47540.1464X20.79820.15895.02410.0000X30.10950.55030.19900.8431X42.71510.219212.39000.0000X50.97900.35952.72340.0089Mean dependent var1.9809S.D. dependent var2.4792Sum squared resid68.239S.E. of

Consider the following regression model YiÃ¢â‚¬â€ž=Ã¢â‚¬â€žÃŽÂ²0Ã¢â‚¬â€¦+Ã¢â‚¬â€¦ÃŽÂ²1X1iÃ¢â‚¬â€¦+Ã¢â‚¬â€¦ÃŽÂ²2X2iÃ¢â‚¬â€¦+Ã¢â‚¬â€¦ÃŽÂ²3X3iÃ¢â‚¬â€¦+Ã¢â‚¬â€¦ÃŽÂ²4X4iÃ¢â‚¬â€¦+Ã¢â‚¬â€¦ÃŽÂ²5X5iÃ¢â‚¬â€¦+Ã¢â‚¬â€¦ui This model has been estimated by OLS. The Gretl output is below. Model 1: OLS, using observations 1-56 coefficient std. error t-ratio p-value const -0.3859 0.5198 -0.7424 0.4613 X1 0.3065 0.2078 1.4754 0.1464 X2 0.7982 0.1589 5.0241 0.0000 X3 0.1095 0.5503 0.1990 0.8431 X4 2.7151 0.2192 12.3900 0.0000 X5 0.9790 0.3595 2.7234 0.0089 Mean dependent var 1.9809 S.D. dependent var 2.4792 Sum squared resid 68.239 S.E. of regression 1.1682 R-squared 0.79814 Adjusted R-squared 0.77795 F(5, 50) 39.539 P-value(F) 0 Log-likelihood -84.995 Akaike criterion 181.99 Schwarz criterion 194.14 Hannan-Quinn 186.7 (5 marks) Construct a 99% confidence interval for ÃŽÂ²4ÃŽÂ²4. (5 marks) Using the critical value method and a significance level of 5%, test H0:ÃŽÂ²2=1H0:ÃŽÂ²2=1 against H1:ÃŽÂ²2<1H1:ÃŽÂ²2<1.

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