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Plotting the growth curve

You saw in the previous exercise that the confidence interval on the growth curve is very tight. You will explore this graphically here by plotting several bootstrap lines along with the growth curve. You will use the plt.semilogy() function to make the plot with the y-axis on a log scale. This means that you will need to transform your theoretical linear regression curve for plotting by exponentiating it.

This is a part of the course

“Case Studies in Statistical Thinking”

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Exercise instructions

  • Plot the data points using plt.semilogy(). The numpy arrays t and bac_area are again in your namespace.
  • Use np.array() to generate time values for plotting the bootstrap lines. Call this t_bs. The time should go from 0 to 14 hours.
  • Write a for loop to plot regression lines corresponding to the first 100 pairs bootstrap replicates. The numpy arrays growth_rate_bs_reps and log_a0_bs_reps that you computed in the last exercise are in your namespace.
    • Compute the growth curve by exponentiating the linear regression line using np.exp().
    • Plot the theoretical line using plt.semilogy() with keyword arguments linewidth=0.5, alpha=0.05, and color='red'.
  • Label the axes and show your plot. Appropriate labels for the respective x and y axes are 'time (hr)' and 'area (sq. µm)'.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Plot data points in a semilog-y plot with axis labeles
_ = ____(____, ____, marker='.', linestyle='none')

# Generate x-values for the bootstrap lines: t_bs
t_bs = ____([____, ____])

# Plot the first 100 bootstrap lines
for i in range(____):
    y = ____(____[i] * ____ + ____[i])
    _ = ____(____, ____, linewidth=____, alpha=____, color=____)
    
# Label axes and show plot
_ = plt.xlabel('____')
_ = plt.ylabel('____')
____
Edit and Run Code

This exercise is part of the course

Case Studies in Statistical Thinking

IntermediateSkill Level
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Take vital steps towards mastery as you apply your statistical thinking skills to real-world data sets and extract actionable insights from them.

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To begin, you'll use two data sets from Caltech researchers to rehash the key points of Statistical Thinking I and II to prepare you for the following case studies!

Exercise 1: Activity of zebrafish and melatoninExercise 2: EDA: Plot ECDFs of active bout lengthExercise 3: Interpreting ECDFs and the storyExercise 4: Bootstrap confidence intervalsExercise 5: Parameter estimation: active bout lengthExercise 6: Permutation and bootstrap hypothesis testsExercise 7: Permutation test: wild type versus heterozygoteExercise 8: Bootstrap hypothesis testExercise 9: Linear regressions and pairs bootstrapExercise 10: Assessing the growth rateExercise 11: Plotting the growth curve

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