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Assessing the growth rate

To compute the growth rate, you can do a linear regression of the logarithm of the total bacterial area versus time. Compute the growth rate and get a 95% confidence interval using pairs bootstrap. The time points, in units of hours, are stored in the numpy array t and the bacterial area, in units of square micrometers, is stored in bac_area.

This exercise is part of the course

Case Studies in Statistical Thinking

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Exercise instructions

  • Compute the logarithm of the bacterial area (bac_area) using np.log() and store the result in the variable log_bac_area.
  • Compute the slope and intercept of the semilog growth curve using np.polyfit(). Store the slope in the variable growth_rate and the intercept in log_a0.
  • Draw 10,000 pairs bootstrap replicates of the growth rate and log initial area using dcst.draw_bs_pairs_linreg(). Store the results in growth_rate_bs_reps and log_a0_bs_reps.
  • Use np.percentile() to compute the 95% confidence interval of the growth rate (growth_rate_bs_reps).
  • Print the growth rate and confidence interval to the screen. This has been done for you, so hit 'Submit Answer' to view the results!

Hands-on interactive exercise

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

# Compute logarithm of the bacterial area: log_bac_area
log_bac_area = ____

# Compute the slope and intercept: growth_rate, log_a0
____, ____ = ____

# Draw 10,000 pairs bootstrap replicates: growth_rate_bs_reps, log_a0_bs_reps
____, ____ = ____(
    ____, ____, size=____
)
    
# Compute confidence intervals: growth_rate_conf_int
growth_rate_conf_int = ____

# Print the result to the screen
print("""
Growth rate: {0:.4f} 1/hour
95% conf int: [{1:.4f}, {2:.4f}] 1/hour
""".format(growth_rate, *growth_rate_conf_int))
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