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## AP®︎/College Statistics

### Course: AP®︎/College Statistics>Unit 5

Lesson 4: Least-squares regression

# Calculating the equation of the least-squares line

You might need: Calculator

## Problem

A stonemason wants to look at the relationship between the density of stones she cuts and the depth to which her abrasive water jet cuts them. The data show a linear pattern with the summary statistics shown below:
meanstandard deviation
$x=$ stone density $\left(\frac{\text{g}}{{\text{cm}}^{3}}\right)$$\overline{x}=2.5$${s}_{x}=0.3$
$y=$ cutting depth $\left(\text{mm}\right)$$\overline{y}=41.7$${s}_{y}=42$
$r=-0.95$
Find the equation of the least-squares regression line for predicting the cutting depth from the density of the stone.
Round your entries to the nearest hundredth.
$\stackrel{^}{y}=$
$+$
$x$
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