MATH 314 Quiz 24

Due on 2026-04-09 by 1:55pm

Download the following dataset into your Quiz 24 repository: finches. Here's the metadata. Please push this dataset along with your ipynb file for Quiz 24.

  1. Fit a linear regression model to predict wing length (winglength) using tail length (taillength).

    a. Make a plotnine plot with taillength on the x-axis and winglength on the y-axis, with a linear regression line going through the data.

    b. Interpret the intercept in context of the data.

    c. Does the intercept make sense in this context? Why or why not?

    d. Interpret the slope in context of the data.

    e. Does the slope make sense in this context? Why or why not?

  2. Fit a linear regression model to predict wing length (winglength) that has unique intercepts by island and a shared slope across tail length (taillength).

    a. Calculate and interpret the intercept for finches from the island San Cristobal in context of the data.

    b. Calculate and interpret the intercept for finches from the island Floreana in context of the data.

    c. Make a prediction for a finch from the island San Cristobal with a tail length equal to the mean tail length for finches from the island San Cristobal.

    d. Make a prediction for a finch from the island Floreana with a tail length equal to the mean tail length for finches from the island San Cristobal.

    e. What from the linear regression output suggests that the predictions from part c. and d. are probably similar?

  3. Fit a linear regression model to predict wing length (winglength) that has unique intercepts and slopes by island across tail length (taillength).

    a. Calculate and interpret the slope for finches from the island Santa Cruz in context of the data.

    b. Calculate and interpret the slope for finches from the island Floreana in context of the data.

    c. Make a prediction for a finch from the island Santa Cruz with a tail length equal to the mean tail length for finches from the island Santa Cruz.

    d. Make a prediction for a finch from the island Floreana with a tail length equal to the mean tail length for finches from the island Santa Cruz.

    e. What from the linear regression output suggests that the predictions from part c. and d. are probably similar?

  4. Challenge (for extra credit: full points on your worst previous quiz). Plot the two models from questions 2. and 3. There should be a line for each island.

  5. If you still have time, work on Homework 12.