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Section 4.2. How Can We Define the Relationship between two sets of Quantitative Data?. Consider the Relationship Between Length and Weight in some Lengths of Channel Iron:. Scatter Plot. Find an Equation by Hand:.

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section 4 2

Section 4.2

How Can We Define the Relationship between two

sets of Quantitative Data?

find an equation by hand
Find an Equation by Hand:
  • Pick two points that define a line of best fit (the points do not have to be part of the data) … how about (19,160) & (56,518)
  • y = mx + b ( slope = m = ) … so m =
  • Find b by plugging in the slope and one of the two points … 160 = 9.68(19) + b … so b = -23.92
  • So y = 9.68x – 23.92 models the relation ship between length (x) and weight (y)
  • What do m & b represent in the data beyond slope and y-intercept?
use the equation
Use the Equation:
  • How much will a 72 length of channel weigh?
  • y = 9.68(72) – 23.92 ≈ 673 lbs.
  • How long would a length of channel be weighing 250 lbs.?
  • 250 = 9.68x – 23.92, x ≈ 28.3 ft.
least squares regression
Least Squares Regression:
  • A least squares regression line minimizes the sum of the squared vertical distance between the observed and predicted value. We name it , pronounced (y – hat)
  • = mx + b … where m = r & b =
  • = 35.8 & Sx= 15.1888

= 319.6 & Sy= 151.4754

r = .998

  • = mx + b … where m = 9.953 & b = -36.72
three cheers for technology
Three Cheers for Technology:
  • Stat … Calc … LinReg ( ax + b )
  • Shazaam! … = 9.956x – 36.833
  • Why is there a difference in the values from doing it by hand?
  • What is the correlation coefficient (r – value)?
  • r ≈ .998
  • Web link to a good graphing calculator regression tutorial youtube: http://www.youtube.com/watch?v=nw6GOUtC2jY
temp elevation correlation
Temp/Elevation Correlation:
  • Find and its correlation coefficient
  • Graph the data and the line of best fit () on your calculator
  • Estimate the temperature on the top of Mt. Shasta … elevation 14,179 ft.
  • Estimate the elevation if the temperature is 40 degrees.
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