Warm – Up CALCULATOR ALL DAY Round to 3 decimal places 1. Log(5) = 2. Log(105) = 3. 10Log(5) 4. ln(5) = 5. e5 = 6. ln(e5) = 7. eln(5)= 0.699 5 LOG and 10x are Inverse Functions 5 1.609 148.413 5 LN and e are Inverse Functions 5

Solving for . Solve each equation for when x = 5. Linear Model: y = 3.82 Exponential Model: y = 0.0186 Power Model: y = 50.5 Power Model: y = 14.5924

Solve each equation for when x = 5. Reciprocal Model: y = 0.2618 (Flip both sides.) Exponential Model: (Perform the Inverse Log function of raising both sides as the exponent of base 10.) y = 6606.9345

Solve each equation for when x = 5. Exponential Model: (Perform the Inverse Natural Log function of raising both sides as the exponent of base ‘e’ .) y = 45.604

Chapter 10 Straightening Relationships We cannot use a Linear model unless the relationship between the two variables is linear. Often we can re-express or straighten bent relationships so that we can fit and then use a simple linear model.

Choosing a Model - Part 1 x y 1 25 2 18 3 14 5 10 6 15 4 20

Choosing a Model - Part 1 For Data that produces a curve and has a response variable that is a ratio of two units, such as mpg, mph, GDP, use the Reciprocal Model = take reciprocal of y var. Take the Reciprocal of all the y’s x y 1 25 2 18 3 14 5 10 6 15 4 20 L1 L2 L3 = 1/y 1 25 .04 2 18 .05556 3 14 .07143 5 10 .1 6 .16667 15 4 .25 20 .33333 LinReg(L1, L3) R2 = 99.8 LinReg(x, 1/y)

PAGE 238 #1,2,3,10(use Reciprocal of y)

PAGE 238 #1,2,3,10 Use reciprocal model