A high school counselor want to look at the relationship between the grade point average (GPA) and the number of absences for students in the senior class this past year. The data show a linear pattern with the summary statistics shown below:

0

The equation for the regression line is \widehat{y}= a+bx

y

=a+bx, where a is the y-intercept and b is the slope.

We can determine the slope from b=b=r\left(\ \frac{s_y}{s_x}\right)r(

s

x

s

y

)

Plugging in the values of rr, s_{y}s

y

and s_{x}s

x

from the table

b = 0.83\Big(\frac{0.7}{2.5}\Big) = 0.2324b=0.83(

2.5

0.7

)=0.2324

a = \overline{y} - b\overline{x} a=

y

−b

x

a = 3.2 - (0.2324) (4)a=3.2−(0.2324)(4)

a = 3.2 - 0.9296 = 2.2704a=3.2−0.9296=2.2704

Plugging the values of a and b in \widehat{y} = a + bx

y

=a+bx and rounding the values of a and b to the nearest hundredths, we get

\widehat{y} = 2.27 + 0.23 x

y

=2.27+0.23x

x=12 units bd= 10 units

step-by-step explanation: