Question

Are good grades in high school associated with family togetherness? A simple random sample

of 142 high-school students was asked how many meals per week (x) their families ate together.
Their responses produced a mean of ¿x = 3.78 meals per week, with a standard deviation of2
sx = 2.2. Researcherss then matched these responses against the students' grade point averages (GPAs). The scatterplot appeared to be
reasonably linear, so they created a regression line. No apparent pattern emerged in the residuals plot. The equation of the line was GPA=2.73+.11(Meals).

What was the mean GPA ?

Answer 1

Since the equation of the line is 2.73 + 0.11, where mathematically we can write this as ˆy = 2.73 + 0.11x; a being 2.73 and b being 0.11.

To obtain the intercept a, we use this equation: y−b¯x =a. Then manipulate the equation to obtain y=a+b¯x and substitute the known values y= 2.73 + 0.11(3.78)

And we get an answer of 3.1458 or rounded off to 3.15. That is the mean GPA.

I hope this helped!