It is believed that educational attainment is higher in countries with higher expenditure on education as a percentage of GDP. Assuming that there is a linear relationship between expenditure on education as a percentage of GDP and percentage of labour force (over 25 years old) with at least post-secondary education for 14 countries in the World Socioeconomic Data, answer the following questions using the dataset labour force2015.xlsx.(a) Calculate the sample correlation coefficient for the data. Comment on its value.(b) Explain your choice of independent and dependent variables.(c) Let y = Percentage of labour force with at least post-secondary education and x = Expenditure on education as percentage of GDP. Use the Excel Data Analysis Add-in to regress y on x. Interpret the regression coefficients. (d) Plot the data and add the estimated regression line. (e) Find the coefficient of determination (R2) for the above estimated regression line and give a full interpretation of the value. (f) Perform a hypothesis test at the 5% significance level for the gradient of the regression line and draw conclusions about whether there is evidence for a relationship between Expenditure on education as percentage of GDP and Percentage of labour force with at least post-secondary education. (g) Produce appropriate plots of the regression residuals to assess the assumptions of the regression model. Consider if there are any patterns in the residuals, which might suggest ways to improve the model. For example, are the residuals normally distributed and do they have constant variance? (h) Predict the percentage of the labour force with at least post-secondary education for Argentina based on the fact that the country's expenditure on education in 2015 was 5.78% of GDP. Produce a 95% confidence interval for this prediction

U Educational attainment, at least completed post-secondary, Country Name population 25+, total (X) Government expenditure on education, total (X of GDP] Romania 17.76323 3.10676 italy 14.9665 4.08169 Spain 29.29108 4.27239 Hungary 28.74177 4.5721 Germany 34.41009 4.80518 Portugal 18.74139 4.68294 Australia 45.34507 5.31196 Netherlands 31.20981 5.34816 Austria 29.14282 5.45675 New Zealand 44.1959 6.34016 Belgium 33.26115 6.53944 Finland 35.09643 7.08008 Sweden 37.21942 7.5483 Norway 38.02254 7.55247