Suppose we are seeking to explain differences in infant mortality rates (the number of infants who died before the age of one, per 1000 live births) across countries. We have data on a range of possible factors for 133 countries. a. In the first model below we examine whether countries see an improvement (reduction) in infant mortality as income (GDP) increases. Y = Infant Mortality Rate. X = Real GDP per capita. Regression Statistics Multiple R 0.678561 R Square 0.460445 Adjusted R Square 0.456327 Standard Error 29.22538 Observations 133 ANOVA if SS MS F ignificance F Regression 1 95484.85 95484.85 111.7929 2.85E-19 Residual 131 111890.1 854.1229 Total 132 207375 Coefficientstandard Err t Stat P-value Lower 95% Upper 95% Intercept 70.7372 3.492166 20.25597 3.49E-42 63.82887 77.64553 Real GDP per Capita -0.00489 0.000463 -10.5732 2.85E-19 -0.00581 -0.00398 Note that we use real GDP per capita as the X variable, not nominal GDP. Why do you think it is important to use GDP per capita in a model that compares across countries? (2 marks) ii. Interpret the coefficients of the intercept and Real GDP per Capita in this model. (3 marks)iii. Perform a test of whether Real GDP per Capita has any impact at all on infant mortality. [4 marks) b. The next model adds a couple of other possible causal factors: average education levels (the percent of children aged 12-17 who are enrolled in secondary school), and number of TV sets per capita. Regression Statistics Multiple R 0.825661 R Square 0.681716 Adjusted R Square 0.671558 Standard Error 21.34031 Observations 98 ANOVA SS MS F gnificance F Regression 3 91689.17 30563.06 67.11125 2.77E-23 Residual 94 42808.43 455.4088 Total 97 134497.6 Coefficienteandard Err t Stat P-value Lower 95% Upper 95% Intercept 87.89528 4.394331 20.00197 1.22E-35 79.17023 96.62032 TV Sets per capita -45.2359 25.69766 -1.76031 0.081608 -96.2591 5.787424 Real GDP per Capita 1997 -0.00034 0.000777 -0.43661 0.663397 -0.00188 0.001203 School enrollment, second -0.62023 0.115853 -5.35357 6.08E-07 -0.85026 -0.3902 i. Write out the equation for the estimated model. (1 mark) ii. Taking note of the definition / units of the School enrolment variable, interpret the -0.62023 coefficient in this output. (3 marks) iii. Perform a test of whether an increase in Real GDP per Capita reduces the infant mortality rate, using the critical value approach. The relevant critical value you need is -1.66. Why do you think your conclusion is different here to the answer found in Part a? (6 marks) iv . When this data was collected (1997), Malawi had 0.01 TV sets per capita, a Real GDP per capita of $500, and a secondary school enrolment rate of 10%. Use the estimated model to predict Malawi's infant mortality rate in 1997. (NB you don't need to calculate the actual value, just show the formula and calculations you would do if you had a calculator).C. Here is a scatter diagram showing the relationship between the Real GDP per Capita variable (X axis) and the dependent variable (infant mortality rate, Y axis). Infant Mortality rate vs Real GDP per capita 160.00 - 140.00 120.00 100.00 - 80.00 60.00 40.00 20.00 0.00 - 0.00 5000.00 10000.00 15000.00 20000.00 25000.00 Based on this graph, what is the problem with the models that have been estimated above? Explain