Question

Peter analyzed a set of data with explanatory and response variables x and y. He concluded the mean and standard deviation for x as 7.8 and 3.70, respectively. He also concluded the mean and standard deviation for y as 12.2 and 4.15, respectively. The correlation was found to be 0.964. Select the correct slope and y-intercept for the least-squares line. Answer choices are rounded to the hundredths place.

Answer 1

The y-intercept is 3.78.

We have given that,

$\overline{x}=7.8 ,S_x=3.70,\\\overline{y}= 12.2,S_y=4.15\\r=0.964$

What is the formula of the slope?

$Slope=r \times\frac{S_y}{S_x} \\\\Slope=0.964\times \frac{4.15}{3.70}\\ Slope=1.08=\overline{y}-slope\:\times \overline{x}\ intercept\\=\overline{y}-slope\:\times \overline{x}\\=12.2-1.08(7.8)\\=3.78$

Therefore the y-intercept is 3.78.

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