Question

Compute the least-squares regression line for predicting y from a given the following summary statistics. Round final answers to four decimal places, as needed.
xbar = 8.8 sx = 1.5 sy = 1.8 ybar = 30.3
r = -0.84
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Regression line equation: y = ______ + _______ x

Answer 1

Answer: Regression line equation:  $\hat{y}=-1.008x+39.1704$

Step-by-step explanation:

Equation of least-squares regression line for predicting y :

$\hat{y}=b_1x+b_o$

, where $\text{Slope} (b_1)=r\dfrac{s_y}{s_x}$ ,  $\text{intercept}(b_0)=\bar{y}-b_1\bar{x}$

Given: $\bar{x}=8.8,\ s_x=1.5,\ s_y=1.8,\ \bar{y}=30.3,\ r=-0.84$

Then,

$b_1=(-0.84)\dfrac{ 1.8}{ 1.5}\\\\\Rightarrow\ b_1=-1.008$

Now,

$b_0=30.3-(-1.008)(8.8)=30.3+8.8704\\\\\Rightarrow\ b_0=39.1704$

Then, Regression line equation:  $\hat{y}=-1.008x+39.1704$