1. The Equation of the Line of Best Fit
How does the calculator calculate the vales for the slope and y- intercept of the line of best fit?
This lesson will go through the process that the calculator uses.
Using this method, and showing all your work, if you complete the following questions correctly and submit them to Mrs. Matthews on Monday Nov. 7th during homeroom, you will receive extra credit.
Write the equation of the line of best fit for the data below.
Calculate and interpret the value of the correlation coefficient.
Car Stopping Distances
Speed (mi/h) 10 15 20 25 30 35 40 45
Stopping Distance (ft) 27 44 63 85
109
136
164
196

2. The Equation of the Line of Best Fit
Write the equation of the line of best fit for the following data.
Step 1: Extend your table
Time
Miles 5 27 10 46 14 71 18 78 22
107

3. The Equation of the Line of Best Fit
Complete the extended table:
Time
Miles
Time●Miles
Time2
Miles2 5 27 10 46 14 71 18 78 22
107
Totals

4. The Equation of the Line of Best Fit
Time
Miles
Miles●Time
Time2
Miles2 5 27
135 25
729 10 46
460
100
2116 14 71
994
196
5041 18 78
1404
324
6084 22
107
2354
484
11449
Totals 69
329
5347
1129
25419

5. Symbols
Let us discus the symbols used in the formula for slope and y-intercept. n = Number of pairs n in this case is… 5 x = Independent variable (usually the 1st variable) In this case the independent variable is… Time y = Dependent variable (usually 2nd variable) In this case the dependent variable is… Miles

6. Symbols
Σ: this symbol (called sigma) means to add up Therefore Σx means to add up all the x-values. In this case Σx = 69 Σy means to add up all the y-values. In this case Σy = 329 Σxy means to add up all the x●y values. In this case Σxy = 5347 Σx2 means to add up all the x2 values. In this case Σx2 = 1129 Σy2 means to add up all the y2 values. In this case Σy2 = (Σx)2 means to add up all the x-values and square the sum. In this case (Σx)2 = 4761 (Σy)2 means to add up all the x-values and square the sum. In this case (Σy)2 =

7. The Equation of the Line of Best Fit
Step 2: Use the following formula to calculate the slope, m. m = nΣxy – Σx Σy nΣx2 – (Σx)2

8. The Equation of the Line of Best Fit
Step 2: Use the following formula to calculate the slope, m. m = nΣxy – Σx Σy nΣx2 – (Σx)2 = 5(5347) – (69)(329) 5(1129) – 4761 = =

9. The Equation of the Line of Best Fit
Step 3: Use the following formula to calculate the y- intercept, b. b = Σy – mΣx n

10. The Equation of the Line of Best Fit
Step 3: Use the following formula to calculate the y- intercept, b. b = Σy – mΣx n = 329 – (2017/442)(69) 5 =

11. The Equation of the Line of Best Fit
After we have found the values of m and b, write the equation of the line in decimal form to the nearest tenth: y = 2017 x y = 4.6x + 2.8

12. The Equation of the Line of Best Fit
r is calculated using the following formula:

13. The Correlation Coefficient