Section 4.2

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# Section 4.2 - PowerPoint PPT Presentation

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

How Can We Define the Relationship between two

sets of Quantitative Data?

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:
• 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:
• 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:
• 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