NUMB3RS - Season 3 - "Contenders"

Regression & Residual Analysis • Change-Point Detection

Algebra 2 / Pre-Calc / StatisticsTI Lesson PDF

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Understanding the Call Data

Let's inspect the call history of Friend A over a 10-day period. We will examine two variables: the total duration of daily calls in minutes ( $L_2$ ) and the total distance spanned by those calls in miles ( $L_3$ ).

Day ( $L_1$ )	1	2	3	4	5	6	7	8	9	10
Total Time ( $L_2$ )	32	19	28	36	17	23	41	22	37	28
Total Distance ( $L_3$ )	51	30	47	56	27	35	65	41	73	54

If we plot Day ( $L_1$ ) vs. Time ( $L_2$ ) or Day ( $L_1$ ) vs. Distance ( $L_3$ ) directly, we don't notice any obvious, abrupt change-points. The parameters look like normal day-to-day fluctuations. We need a more sophisticated method to find a signature shift.

Model LineResidual Bars

Interactive Day Inspector: Day 8

Shift Signature

Talk Time (x)

22 min

Distance (y)

41 mi

Predicted (ŷ)

37.1 mi

Residual value

+3.9

Mathematical Breakdown:

Predicted value: ŷ = 1.73(22) - 0.96 = 37.1

Residual: y - ŷ = 41 - 37.1 = 3.9