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Statistics and probability

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, equals stone density left parenthesis, start fraction, start text, g, end text, divided by, start text, c, m, end text, cubed, end fraction, right parenthesisx, with, \bar, on top, equals, 2, point, 5s, start subscript, x, end subscript, equals, 0, point, 3
y, equals cutting depth left parenthesis, start text, m, m, end text, right parenthesisy, with, \bar, on top, equals, 41, point, 7s, start subscript, y, end subscript, equals, 42
r, equals, minus, 0, point, 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, with, hat, on top, equals
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
plus
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text
x
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