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Grokking the Data Science Interview

Regression for the DS Interview

Explore how to accurately interpret regression coefficients in data science interviews, including linear and logistic models. Learn to explain unit meanings, statistical significance, odds ratios, and the importance of avoiding causal claims without evidence. Understand how to identify potential confounders, model limitations, and properly communicate insights relevant to interview questions.

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When an interviewer asks, "Walk me through what this model shows," focus on interpreting the regression coefficients, explaining their units, and identifying the limitations of the results rather than describing the estimation procedure.

The interviewer provides output summaries from two models fitted using statsmodels. The first is an ordinary least squares (OLS) regression model predicting weekly spending in dollars. The second is a logistic regression model predicting whether a subscription was renewed. The following excerpts show the model outputs:

                            OLS Regression Results
==============================================================================
Dep. Variable:           weekly_spend   R-squared:                       0.310
Model:                            OLS   Adj. R-squared:                  0.309
==============================================================================
                      coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
Intercept         120.0000      6.020     19.934      0.000     108.200     131.800
support_tickets    -8.0000      2.092     -3.824      0.000     -12.100      -3.900
premium_user       42.0000      8.163      5.145      0.000      26.000      58.000
==============================================================================
                           Logit Regression Results
==============================================================================
Dep. Variable:                renewed   Pseudo R-squ.:                  0.0150
Model:                          Logit
==============================================================================
                      coef    std err          z      P>|z|      [0.025      0.975]
------------------------------------------------------------------------------
Intercept          -2.2000      0.153    -14.379      0.000      -2.500      -1.900
premium_user        0.6900      0.179      3.855      0.000       0.340       1.040
==============================================================================
A representative excerpt

When explaining regression results during an interview, focus on the estimates relevant to the question and omit unrelated output.

A weak answer says that support tickets cause customers to spend eight dollars less, then calls R2=0.31R^2=0.31 a 31% chance that the model is correct. Both claims outrun the output. The coefficient describes an adjusted association in the observed data. R2R^2 describes fit to variation in the outcome, not causal validity or probability that a prediction will be right.

An effective interpretation begins by identifying the outcome variable and the units of each coefficient. In the linear regression model, each additional support ticket is associated with an $8 decrease in expected weekly spending, holding the other included predictors constant. The 95% confidence interval for the support-ticket coefficient excludes zero, indicating ...