Formula of a regression line / Least Squares Regression Line
What should be discussed when using
- Gradient
- y-intercept
- relate to context
On
Regresion line of Y on X is the normal regression line, {X as list 1, Y as list 2} Regression line of X on Y is the inverse, {X as list 2, Y as list 1}
Examples
Table --> Calculator --> Graph --> Graph w/ Regression Line
| Variable | Data | |||||
|---|---|---|---|---|---|---|
| Time (minutes) | 5 | 10 | 15 | 20 | 25 | 30 |
| Temperature (C) | 87 | 78 | 69 | 56 | 53 | 41 |
After Calculation:
since y = ax+b, substituiting in a ad b creates a linear line, this is the line of best fit ad can be plotted as seen below
Graph --> Table/Calculator --> Graph w/ Regression Line
Interpret the regression line.
Translate to Calculater (X = List 1, Y = List 2)
dont use the y intercept (b), as this graph starts at 2 Find Value at “2” using Analyse —> Trace (make sure zoomed out to where point is otherwise domain error) (plot the new line of best fit))
Interpret Regression Line
As the Age of a child increases, it’s Nap Length decreases, this is moderately correlative, given that the “R” Value of this line is -0.70 indicating a Moderate Negative Correlation.
References
Mr. Hansen page=26