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 = 𝑦 2 − 𝑦 1 𝑥 2 − 𝑥 1 ) … so m = 518−160 56−19 ≈9.68
Find b by plugging in the slope and one of the two points … 160 = 9.68(19) + b … so b =
So y = 9.68x – 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) – ≈ 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 𝑦 , pronounced (y – hat)
𝑦 = mx + b … where m = r ∙ 𝑠 𝑦 𝑠 𝑥 & b = 𝑦 −𝑚 𝑥
𝑥 = 35.8 & Sx =
𝑦 = & Sy =
r = .998
𝑦 = mx + b … where m = & b =

7. Three Cheers for Technology:
Stat … Calc … LinReg ( ax + b )
Shazaam! … 𝑦 = 9.956x –
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:

8. Temp/Elevation Correlation:
Temperature
1542 ft
74 F
2238 ft
73 F
5426 ft
70 F
8634 ft
58 F
Find 𝑦 and its correlation coefficient
Graph the data and the line of best fit ( 𝑦 ) 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.