Analyze Town Temperatures and Select Predictors for NYC

A pandas DataFrame contains (N) daily temperature observations for NYC and (P\ge5) town columns. Implement:

q1_q5(df) -> list
q6(df) -> list[str]

q1_q5(df) must return exactly this five-element list:

[
 largest_std_column,
 rounded_conditional_median,
 rounded_absolute_slope_sum,
 best_single_town,
 [best_pair_town_1, best_pair_town_2]
]

q6(df) must return exactly five town names in greedy selection order.

Constraints & Assumptions

• The DataFrame has at least one row, unique string column names, a column named NYC, a column named Town2, and at least five non-NYC columns.
• All cells are finite, numeric, and nonmissing. NYC is the response and every other column is a candidate town.
• Use population standard deviation (ddof=0). If columns tie for the largest standard deviation, return the lexicographically smallest column name. This comparison includes NYC.
• Every regression includes an intercept and is scored by in-sample mean squared error on all supplied rows.
• Break exact MSE ties lexicographically by town name or by the ordered two-town tuple.
• “Round” means nearest integer, with exact half values rounded away from zero.
• If no row has Town2 between 90 and 100 inclusive, raise ValueError.
• A constant predictor has slope zero. For rank-deficient multivariate designs, use the minimum-norm least-squares solution; scoring is based on its predictions.

Part 1 — Variability and conditional median

Set largest_std_column to the column with the largest population standard deviation. Set rounded_conditional_median to the median NYC value among rows where 90 <= Town2 <= 100, rounded once.

What This Part Should Cover

• Population standard deviation across rows for every column, including NYC, with the stated lexicographic tie rule.
• Inclusive Town2 filtering, the required empty-subset error, and one half-away-from-zero rounding step.
• Placement of these two outputs in positions 0 and 1 of the returned list.

Part 2 — Single-town regressions

Fit one separate simple linear regression per candidate town. Set rounded_absolute_slope_sum to the sum of the absolute slope coefficients, rounded once after summing. Set best_single_town to the town whose single-predictor model has the lowest MSE.

What This Part Should Cover

• A distinct intercept-bearing fit for each non-NYC column and a zero slope for a constant predictor.
• Absolute slopes summed before the single required rounding operation.
• In-sample MSE comparison with the stated town-name tie rule and outputs in positions 2 and 3.

Part 3 — Best pair

Fit every unordered two-town linear model. Return the lowest-MSE pair as two lexicographically ordered names.

What This Part Should Cover

• Enumeration of each unordered town pair exactly once and a joint two-predictor fit with an intercept.
• Minimum-norm least squares for a rank-deficient pair and MSE scoring from its predictions.
• Lexicographic ordering within the pair, tuple-based score ties, and the nested list in position 4.

Part 4 — Approximate best five-town subset

For q6, begin with no predictors. At each of five steps, refit each model formed by the already selected towns plus one remaining town. Append the town producing the lowest MSE, using its name to break an exact tie. Greedy selection is an approximation and need not equal the globally best five-town subset.

What This Part Should Cover

• Five forward-selection rounds, with every remaining candidate refit alongside the already selected towns at each round.
• In-sample MSE and the exact town-name tie rule at every selection step.
• Exactly five distinct names returned in selection order, plus a clear statement that the greedy result is not guaranteed globally optimal.