Question

A high school counselor wants 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:
mean
standard deviation
I= = of absences
z = 5.0
Sz = 1.2
y= GPA
Y = 2.9
Sy = 0.3
p = -0.65
Find the equation of the least-squares regression line for predicting GPA from the number of absences.
Round your entries to the nearest hundredth.
y =
+
22
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Answer 1

Least-squares regression is used to find the equation of best fit of a linear model

The equation of the least-squares regression line for predicting GPA from the number of absences is $\mathbf{y = 3.71 - 0.16x}$

The given parameters are:

$\mathbf{\bar x =5.0}$

$\mathbf{s_x =1.2}$

$\mathbf{\bar y=2.9}$

$\mathbf{s_y=0.3}$

$\mathbf{r =-0.65}$

The equation of the least-squares regression line is represented as:

$\mathbf{y = a + bx}$

Where:

$\mathbf{b = r \times (\frac{s_y}{s_x}) \ and\ a = \bar y - b \bar x}$

So, we have:

$\mathbf{b = -0.65 \times (\frac{0.3}{1.2})}$

$\mathbf{b = -0.1625}$

$\mathbf{a = \bar y - b \bar x}$

$\mathbf{a = 2.9 - (-0.1625) \times 5.0}$

$\mathbf{a = 3.7125}$

Substitute values for a and b in $\mathbf{y = a + bx}$

So, we have:

$\mathbf{y = 3.7125 - 0.1625x}$

Approximate

$\mathbf{y = 3.71 - 0.16x}$

Hence, the equation of the least-squares regression line for predicting GPA from the number of absences is $\mathbf{y = 3.71 - 0.16x}$

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