Problem 3. (10 points) Remaining time: 660:58 (min:sec) In 1888, a survey was taken of Swiss provinces in an attempt to measure the relationships between several different variables. One relationship of interest is the relationship between the education rate of a province and the province's infant mortality. A sample of 15 different provinces was taken. In each province, the percent of individuals in the province who had education beyond primary school was measured ("Education") as well as the provinces' infant mortality rate (live births that lived less than one year, "Infant"). This data is shown in the two vectors below. To use the data, copy and paste the following lines into your R or RStudio console. Infant=c(20.3,20.2,20,20.2,22.7, 18,24.5,23.8,18.9,20.5,20,22.4,22.4, 16.7,15.1) Education=c(7,28,8,3,12,53,6,8, 13, 11,9,3,3, 12,2) a. Compute the correlation between the percent of individuals who had education beyond primary school and infant mortality rate. Answer: Round to at least five decimals if necessary b. State the regression equation used to express the infant mortality rate (Y) as a linear function of the percent of individuals who had education beyond primary school (X). Report all decimals printed by R. Yi = c. Which of the following is the best interpretation of 81 in the above regression equation? A. The percent of individuals who had education beyond primary school for a province with an infant mortality rate of 0 units is, on average, $1% B. As the percent of individuals who had education beyond primary school increases by 1%, infant mortality decreases by Bj units C. As the percent of individuals who had education beyond primary school increases by 1%, infant mortality rate decreases on average by 1 unit D. As the percent of individuals who had education beyond primary school increases by 1%, infant mortality increases on average by B1 units E. As the percent of individuals who had education beyond primary school increases by 81%, infant mortality rate decreases by 1 unit OF. The infant mortality for a province with 0% percent of individuals who had education beyond primary school is, on average, B1 d. The coefficient of determination tells us that % of the variation in infant mortality is explained by its linear relationship with the percent of individuals who had education beyond primary school v . Round to at least five decimals if necessary e. Consider the fourth province in the dataset, which is a province that has a percent of individuals who had education beyond primary school of 3% and an infant mortality of 20.2 units. Compute the residual for this province. e = Round to at least five decimals if necessary preview answers