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Course: Statistics and probability > Unit 5

Lesson 4: Least-squares regression equations
Math
Statistics and probability
Exploring bivariate numerical data
Least-squares regression equations
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Calculating the equation of the least-squares line

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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 (gcm3)x¯=2.5sx=0.3
y= cutting depth (mm)y¯=41.7sy=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.
y^=
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
+
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi
x