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Analyze Temperatures and Update Regression

Two SigmaData Scientist · Online Assessment
MediumData ScientistOnline AssessmentMachine Learning

Last updated

This question evaluates proficiency in time-series and statistical analysis (defining volatility and similarity metrics), supervised regression modeling with mean squared error evaluation, greedy feature selection, and streaming/no-intercept linear regression updates.

You are given historical daily temperature data for New York City and several nearby towns. Each row contains a date, the NYC temperature, and the temperature for each town on that date.

Answer the following:

  1. Volatility analysis
  • Determine which town has the largest temperature fluctuation over time.
  • Clearly define the metric you use for fluctuation.
  1. Similarity analysis
  • Determine which town's temperature pattern is most similar to NYC's.
  • Clearly define the similarity metric you use.
  1. Prediction task
  • Use the towns' temperature data to predict NYC temperature.
  • Train a regression model and evaluate it using mean squared error, or MSE.
  1. Greedy feature selection
  • Given a target number k, choose k towns to use as features.
  • Start with no selected towns.
  • At each step, add the town that gives the largest reduction in validation MSE when combined with the already selected towns.
  • Return the selected towns and the final MSE.
  1. No-intercept linear regression
  • Implement simple linear regression without an intercept for a single predictor x and target y.
  • First solve the batch case, where all data is available at once.
  • Then solve the streaming case, where (x, y) pairs arrive one at a time and the current slope must be updated without recomputing from scratch over all past data.