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Worksheet: Logistic Regression Model

Q1:

The data shows how the population of an animal species changed over 12 years.

Number of Years 1 2 3 4 5 6 7 8 9 10 11 12
Population 57 98 206 367 482 501 526 534 547 556 557 559

Use a calculator to calculate the regression equation 𝑦 = 𝑐 1 + π‘Ž 𝑒 βˆ’ 𝑏 π‘₯ . Round the values of π‘Ž , 𝑏 , and 𝑐 to two decimal places.

  • A 𝑦 = 3 6 . 9 9 1 + 5 4 9 . 2 7 𝑒 1 . 0 6 π‘₯
  • B 𝑦 = 3 6 . 9 9 1 + 5 4 9 . 2 7 𝑒 βˆ’ 1 . 0 6 π‘₯
  • C 𝑦 = 5 4 9 . 2 7 1 + 1 . 0 6 𝑒 βˆ’ 3 6 . 9 9 π‘₯
  • D 𝑦 = 5 4 9 . 2 7 1 + 3 6 . 9 9 𝑒 βˆ’ 1 . 0 6 π‘₯
  • E 𝑦 = 1 . 0 6 1 + 5 4 9 . 2 7 𝑒 βˆ’ 3 6 . 9 9 π‘₯

Use your equation to determine the carrying capacity of the population. Give your answer as a whole number.

Q2:

Some data sets can be modeled with nonlinear regression models.

Which scatterplot shows data that can be best modeled by logistic regression?

  • A
  • B
  • C
  • D

Which formula models the relationship between π‘₯ and 𝑦 in such a data set?

  • A 𝑦 = 𝑐 1 βˆ’ π‘Ž 𝑒 𝑏 π‘₯
  • B 𝑦 = 𝑐 1 βˆ’ π‘Ž 𝑒 βˆ’ 𝑏 π‘₯
  • C 𝑦 = 𝑐 1 + π‘Ž 𝑒 𝑏 π‘₯
  • D 𝑦 = 𝑐 1 + π‘Ž 𝑒 βˆ’ 𝑏 π‘₯