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Section 4.2

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

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  1. Section 4.2 How Can We Define the Relationship between two sets of Quantitative Data?

  2. Consider the Relationship Between Length and Weight in some Lengths of Channel Iron:

  3. Scatter Plot

  4. 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?

  5. 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.

  6. 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

  7. 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

  8. 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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