De Analytical Questions For this portion of the prob folder on Canvas. The file con interviewed in the Demographic need to load the tidyverse and The Demographic and Health Survey i ity and health behavior. The variables in 1. Consider the data on hours studied per week and final grades in EC 320 from a sample of four Variable Name students: (2 points each) Student Hours Studied Final Grade id educ peduc kids Hinata Michelle 72% 97% Jerry 43% Jorge 84% (a) Suppose that you want to use the data to learn about the effect of studying on grades. must provide Write down a simple linear regression model tailored to your objective. tors. For full (b) Calculate the parameter estimates for the intercept (B1) and slope (32) using the OLS answers. You formulas from class. e file types on (c) Interpret B1. What does this parameter estimate tell us? (d) Interpret B2. What does this parameter estimate tell us? (e) Calculate the coefficient of determination ( R2) for the regression you estimated. What does it tell us about the relationship between studying and grades? (f) What is the predicted final grade for a student who studies 5 hours per week? (g) Based on the regression you estimated, how many hours would a student have to study to expect a score of 100%? 2. Consider the predicted values of Y; from a simple linear regression of Y; on Xi, which we refer to as Y. Prove that the sample mean of Y; is equal to the sample mean of Yi (i.e. Y). (3 points) 3. Consider the residuals (ui) from a simple linear regression. Prove that the sample mean of ui is