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=2Γ—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=3.1Γ—0.5, estimate the value of 𝑦 when π‘₯ is equal to 4.

  • A0.19375
  • B5.772
  • C0.3677
  • D6.2
  • E3.1625

Q3:

Given the exponential regression model 𝑦=4Γ—1.2, determine the value of 𝑦 when π‘₯ is equal to 0.

Q4:

Given the quadratic regression model 𝑦=3π‘₯βˆ’5π‘₯+2, calculate the value of 𝑦 when π‘₯ is equal to 2.7.

Q5:

Given the quadratic regression model 𝑦=βˆ’π‘₯+5.2π‘₯βˆ’2.1, calculate the value of 𝑦 when π‘₯ is equal to 3.

Q6:

The values (0,1), (1,2), (2,3.5), and (3,4) of the ordered pair of variables (π‘₯,𝑦) are observed in an experiment. Use least-squares quadratic regression to find the values of π‘Ž, 𝑏, and 𝑐 for which the model 𝑦=π‘Žπ‘₯+𝑏π‘₯+π‘οŠ¨ best fits the data.

  • Aπ‘Ž=0.815, 𝑏=1.147, and 𝑐=βˆ’0.135
  • Bπ‘Ž=βˆ’0.125, 𝑏=1.425, and 𝑐=0.925
  • Cπ‘Ž=0.925, 𝑏=1.425, and 𝑐=βˆ’0.125
  • Dπ‘Ž=0.125, 𝑏=βˆ’1.425, and 𝑐=0.925
  • Eπ‘Ž=1.425, 𝑏=βˆ’0.125, and 𝑐=0.925

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