Answer following in R Studio

#3) A mathematics placement test is given to all entering freshmen at a small #college. A student who receives a grade below 35 is denied admission to the #regular mathematics course and placed in a remedial class. The placement test #scores (test) and the final grades (grades) for 30 students who took the #regular course were recorded as follows:

test <- c(65, 70, 45, 50, 35, 35, 40, 55, 65, 35, 60, 90, 35, 75, 90, 80, 60, 60, 60, 40, 55, 50, 65, 50, 75, 80, 80, 45, 70, 60) grade <- c(60, 70, 50, 53, 41, 61, 56, 68, 36, 11, 70, 79, 59, 54, 70, 91, 48, 71, 71, 47, 53, 68, 57, 79, 60, 65, 70, 55, 65, 65)

#a) Plot a scatter diagram

#b) Find the equation of the regression line to predict course grades from #placement test scores.

#c) Graph the line of the scatter diagram

#d) Plot the residuals vs predicted values. Does the linear model make sense based #off of this information?

#e) Determine if the residuals are normally distributed.

#f) What is the 95% interval range for the possible grades based off of this #sample?

#g) What is the 95% interval of the average grade for a test that scored 60?

#h) Should the placement into remedial course be changed to below 60 instead of #below 35?