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`

Explanation:

Equation of least-squares regression line for predicting y :

`\hat{y}=b_1x+b_o`

, where
`\text{Slope} (b_1)=r(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)( 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`