3. "Does education affect a nation's democracy" is always a core issue in political science and international relations. To figure out the issue, a teacher Mateus collected the democracy score and proportion of educated citizens of several countries. A nation's democracy score is ranging from 0 to 10, in which ( represents no democracy and 10 represents fully democracy. Then, Mateus conducted a regression analysis to study the cause and effect of education on democracy. The table below is the regression results using the software EXCEL.Predictor Coef SE Coef T P Constant 2.726 0.886 3.08 0.006 Education 0.124 0.021 5.90 0.000 Analysis of Variance Source DF SS MS F P Regression 10354 10354 15.46 0.001 Residual 18 12054 670 Total 19 22408 (a) How many countries were in the sample? (1 point) (b) What is the dependent variable "Y", the proportion of educated citizens or democracy score? (2 points) (c) What is the independent variable "X", the proportion of educated citizens or democracy score? (2 points) (d) Use the information above, write down the regression equation "y = a + bx". (5 points) (e) Determine the coefficient of determination. (5 points) (f) At the 0.05 significance level, does the evidence suggest there is a positive effect of education on a nation's democracy? Why? Use the hypothesis testing to support your answer. (8 points)