Question

4) A math instructor at Futurama Community College has found, based on studies from the years 3000 to 3009, that the number of students enrolled in Relevant Applied Math in a given year can be predicted from the regression equation ŷ = 494 - 26%, (where z is the number of years after 3000; x = 4, for example, means 3004) and that 82.33 of the variation in the number of students enrolled can be explained by the year. a) What is the slope of the regression line? (3) b) What is the value of ra, the coefficient of determination? (3) c) Use the regression equation to predict the number of students enrolled in the course in 3008. (3) d) The instructor's data show 279 students enrolled in 3008. the regression equation? Explain. (2) Is there a mistake in

Answer 1

The regression equation is

y = 494 - 26z

The form of the linear equation is

y = m x + b

m is the slope

b is the initial amount (y-intercept)

By comparing them

The slope is -26

At 3008 x = 8

Substitute z by 8 in the equation to find the number of students

y = 494 - 26(8)

y = 286

So 279 can not be the number of students in 3008 because the number of students is 286

The rate of decreasing must be 26 (the slope)

So the student will decrease by 208 in 8 years

Then 494 - 208 = 286 not 279