The Equation of the Line of Best Fit

The Equation of the Line of Best Fit How does the calculator calculate the vales for the slope and yintercept 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 Tuesday April 2 nd during homeroom, you will receive extra credit. (a) Write the equation of the line of best fit for the data below. (Round to the nearest tenth) (b) Interpret the value of the slope and y-intercept. 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

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

The Equation of the Line of Best Fit Complete the extended table: Totals Time Miles Time●Miles Time 2 5 27 10 46 14 71 18 78 22 107 Miles 2

The Equation of the Line of Best Fit Time Miles●Time 2 Miles 2 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

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 1 st variable) In this case the independent variable is… Time y = Dependent variable (usually 2 nd variable) In this case the dependent variable is… Miles

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 Σx 2 means to add up all the x 2 values. In this case Σx 2 = 1129 Σy 2 means to add up all the y 2 values. In this case Σy 2 = 25419 (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 = 108241

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

The Equation of the Line of Best Fit Step 2: Use the following formula to calculate the slope, m. m = nΣxy – Σx Σy nΣx 2 – (Σx)2 = 5(5347) – (69)(329) 5(1129) – 4761 = 4034 884 = 2017 442

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

The Equation of the Line of Best Fit Step 3: Use the following formula to calculate the yintercept, b. b = Σy – mΣx n = 329 – (2017/442)(69) 5 = 1249 442

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 + 1249 442 y = 4. 6 x + 2. 8