Worksheet: Logistic Regression Model

In this worksheet, we will practice using logistic regression to find a logistic growth function to model data.

Q1:

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 𝑥 and 𝑦 in such a data set?

  • A𝑦=𝑐1+𝑎𝑒
  • B𝑦=𝑐1𝑎𝑒
  • C𝑦=𝑐1𝑎𝑒
  • D𝑦=𝑐1+𝑎𝑒

Q2:

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

Number of Years123456789101112
Population5798206367482501526534547556557559

Use a calculator to calculate the regression equation 𝑦=𝑐1+𝑎𝑒. Round the values of 𝑎, 𝑏, and 𝑐 to two decimal places.

  • A𝑦=36.991+549.27𝑒
  • B𝑦=549.271+1.06𝑒
  • C𝑦=1.061+549.27𝑒
  • D𝑦=549.271+36.99𝑒
  • E𝑦=36.991+549.27𝑒

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

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