1.Now use multipleregression to explore the relationship of annual growth of per capita GDP over 1990-2000 (Y) with, mean temperature over 1990-2000 (X1), and mean precipitation over 1990-2000 (X2). You may use Data Analysis Tool Pack for this. Based on the excel regression output, first write down the estimated regression equation,then interpret the estimated coefficients on the mean temperature over 1990-2000 (X1), and meanprecipitation over 1990-2000 (X2).Carry out any relevant two-tailed hypothesis tests using the p-valueapproach at the 5% significance level, and an overall significance test using the p-valueapproach. Carefully interpret your hypothesis test results.

2.Write down a paragraph or two to illustrate: a) why the hypothesis test is required in the above regression analysis (either simple or multiple); b) the underlying mechanism/intuition of a two-tailed hypothesis test in the context of regression analysis. Aid your illustration with appropriate diagrams.

3.Carefully interpret the adjusted R-squared in the multipleregression analysis.

4.If you could request additional data to study the factors that influence the annual growth of per capita GDP, what extra variables would you request? Illustratetwosuch variables. Carefully explain why you choose these two variables (by drawing evidence from the literature such as journal articles, newspapers, et al), types of your proposed variables (e.g. numerical or categorical), and how each of your proposed variables will be measured in the regression model.

country per_cap_GDP2000 growth1990_2000 tem1950_1960 pre1950_1960 tem1990_2000 pre1990_2000 Nigeria 6.341999468 0.017646708 26.52577 13.88756 26.85172 13.39307 Panama 8.309018174 3.343584973 24.68316 28.04099 25.11478 27.48667 United Arab Emirates 10.41305497 0.351553339 26.84328 1.631635 26.91433 1.263214 Spain 9.596491202 2.487687259 13.48391 6.651904 14.41149 6.297207 Austria 10.10905589 2.300388065 7.549002 9.950752 7.952092 9.221741 Canada 10.09370492 0.582056958 4.841475 9.364386 5.296148 9.385453 Vanuatu 7.2934069 1.483790792 24.15511 27.481 24.62386 25.28607 Australia 9.984110761 2.135885605 15.86288 9.355159 15.80989 7.964385 Sierra Leone 4.932303899 -2.469349752 25.70401 28.29842 26.19973 25.13283 Brunei 9.798824364 -0.428450843 27.20606 30.216 27.06742 26.36298 Ghana 5.554783345 1.456127111 26.31561 14.2106 26.67841 12.75037 Fiji 7.638472188 1.673783596 23.89741 31.08469 24.03207 25.13651 Egypt 7.279647225 2.512322923 21.03608 0.3591493 21.2031 0.6710021 Turkey 8.375048385 2.602163169 12.03383 5.847577 12.12031 6.115713 Belgium 10.04505372 2.029001451 9.626793 7.704759 10.52248 7.875272 Cote d'Ivoire 6.478979435 -1.23001107 26.24332 15.25539 26.26308 12.65963 Iran 7.420584576 2.423024302 13.79623 3.894315 14.32119 3.533688 India 6.094278759 3.585117687 25.23642 12.74809 25.26296 11.98164 Suriname 7.607024507 -1.087064319 26.61093 22.14153 26.69649 21.5842 Senegal 6.404656503 0.055498592 26.9184 9.227755 27.44442 6.163564 Togo 5.711110209 -0.37610378 26.07221 12.79692 26.32782 11.59565 Rwanda 5.563669533 1.252000313 19.12939 10.76035 20.2585 10.81682 Peru 7.578446198 1.279218094 13.26135 8.056942 14.05118 8.142179 Mauritius 8.276159434 4.281374685 24.04545 16.54273 23.99242 14.99573 Philippines 6.978035781 0.530769128 25.38977 24.72692 25.64058 23.83464