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

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
- Web link to a good graphing calculator regression tutorial youtube: http://www.youtube.com/watch?v=nw6GOUtC2jY

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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