Bio-Tech
NOTES FOR LINEAR REGRESSION
Introduction:
Prediction?
________________________________________________________
____________________________________________________________________________
Objective: ___________________________________________________________________
Bivariate data _____________________________________________
Warm-Up: 1. Write an equation of the line that has slope ¾ and y-intercept -2. ___________________
2. Write an equation of the line that passes through the y-axis at 3 and has slope of -4. ___________________
3. Write an equation of the line shown I the graph on the screen. __________________
4. If a line passes through (0, 5) and (2, 9), then the slope is ______ and an equation of the line is __________.
5. Write an equation of the line which passes through (-3, 8) and has a slope of -2. ______________________.
Equation of a line in “slope-intercept” form _____________________ or
_____________________________ (statistics books)
“Linear Regression” ____________________________________________________________
Summation
Mean
∑𝑥
______________________________________
𝑥̅ ______________________________________________
Predicted value of y 𝑦̂ ____________________________________
All regression lines pass through the point ______________________
Table set-up (fill in the headings of the columns)
x
y
Formula for the slope (b) of the regression line ____________________
Bio-Tech Notes p. 2
Example problem: Fill in each cell in the table. Calculate the means for x and y.
Interesting fact: ∑(𝑥 − 𝑥̅ ) = 0 This means that you can check the 3rd and 4th column values
by adding them and checking to see if the sum is equal to 0!
X
3
7
10
15
18
Y
16
45
82
102
116
̅
𝒙−𝒙
(𝒙 − 𝒙
̅)(𝒚 − 𝒚
̅)
̅
𝒚−𝒚
∑
Calculate the slope of this line
𝑏=
∑(𝑥−𝑥̅ )(𝑦−𝑦̅)
∑(𝑥−𝑥̅ )2
(𝒙 − 𝒙
̅ )𝟐
∑
=
Regression line must pass through the (mean, mean) ______________
Substitute into the equation and solve for ‘a’
Equation ___________________________
Use your equation to find the possible y-value when the x = 12. _________
Use your equation to find the possible value of x when y = 32. _________
Use your equation to predict y when x = 20. ______
Use your equation to predict x when y = 150. ________
(𝒚 − 𝒚
̅ )𝟐
Bio-Tech Notes p. 3
Correlation Coefficient ‘r’ ____________________________________
𝑟=
𝑧 𝑠𝑐𝑜𝑟𝑒 =
∑(𝑥 − 𝑥̅ )2
√
𝑠=
𝑛−1
Notes for finding ‘r’:
Notes for key-strokes on calculators:
∑ 𝑧𝑥 𝑧𝑦
𝑛−1
𝑣𝑎𝑙𝑢𝑒 − 𝑚𝑒𝑎𝑛
𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛