Worksheet: Exponential Regression Model

In this worksheet, we will practice using the exponential regression features on a graphing calculator, rather than algebraic techniques, to model data exhibiting exponential growth or decay.

Q1:

An exponential model with the equation 𝑦 = 2 × 1 . 3 is fitted to a set of data. The point ( 2 . 5 , 5 ) is part of the original data set to which the model was fitted. Calculate, to the nearest hundredth, the residual for this point.

Q2:

Given the exponential regression model 𝑦 = 3 . 1 × 0 . 5 , estimate the value of 𝑦 when 𝑥 is equal to 4.

  • A 0.19375
  • B 6.2
  • C 5.772
  • D 0.3677
  • E 3.1625

Q3:

Given the exponential regression model 𝑦 = 4 × 1 . 2 , determine the value of 𝑦 when 𝑥 is equal to 0.

Q4:

Given the quadratic regression model 𝑦 = 3 𝑥 5 𝑥 + 2 , calculate the value of 𝑦 when 𝑥 is equal to 2.7.

Q5:

Given the quadratic regression model 𝑦 = 𝑥 + 5 . 2 𝑥 2 . 1 , calculate the value of 𝑦 when 𝑥 is equal to 3.

Q6:

The values ( 0 , 1 ) , ( 1 , 2 ) , ( 2 , 3 . 5 ) , and ( 3 , 4 ) of the ordered pair of variables ( 𝑥 , 𝑦 ) are observed in an experiment. Use least-squares quadratic regression to find the values of 𝑎 , 𝑏 , and 𝑐 for which the model 𝑦 = 𝑎 𝑥 + 𝑏 𝑥 + 𝑐 best fits the data.

  • A 𝑎 = 0 . 8 1 5 , 𝑏 = 1 . 1 4 7 , and 𝑐 = 0 . 1 3 5
  • B 𝑎 = 0 . 1 2 5 , 𝑏 = 1 . 4 2 5 , and 𝑐 = 0 . 9 2 5
  • C 𝑎 = 1 . 4 2 5 , 𝑏 = 0 . 1 2 5 , and 𝑐 = 0 . 9 2 5
  • D 𝑎 = 0 . 1 2 5 , 𝑏 = 1 . 4 2 5 , and 𝑐 = 0 . 9 2 5
  • E 𝑎 = 0 . 9 2 5 , 𝑏 = 1 . 4 2 5 , and 𝑐 = 0 . 1 2 5

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