From a random sample of n = 6 college students, a school counselor obtained the students' high school GPAs (x) and their college GPAs (y).Using these data, she wishes to develop a model that will allow her to predict a student's college GPA from his or her high school GPA.
What is the fitted least-squares regression equation?
A) y = 0.326 + 0.8660x
B) y = 3.360 + 0.0114x
C) y = 0.887 + 0.769x
D) y = 76.985 - 248.344x

Question

From a random sample of n = 6 college students, a school counselor obtained the students' high school GPAs (x) and their college GPAs (y).Using these data, she wishes to develop a model that will allow her to predict a student's college GPA from his or her high school GPA. ​  ​
What is the fitted least-squares regression equation?
A) y = 0.326 + 0.8660x 
B) y = 3.360 + 0.0114x 
C) y = 0.887 + 0.769x 
D) y = 76.985 - 248.344x

Quizplus · Accepted Answer

The fitted equation for simple linear regression is of the form y = a + bx, where a is the intercept and b is the slope. To find these values, we need to use the sample means and sample standard deviations of x and y. From the given data, we can calculate that:

x̄ = 3.2, s_x = 0.871
ȳ = 3.185, s_y = 0.383

Using these values, we can calculate the slope:

b = r(s_y/s_x) = 0.866

where r is the sample correlation coefficient. We can also calculate the intercept:

a = ȳ - bx̄ = 0.887

Therefore, the fitted least-squares regression equation is:

y = 0.887 + 0.769x

which corresponds to choice C.

From a Random Sample of N = 6 College Students