Two-Variable Data and Probability flashcards

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Association versus causeScatterplots and Association: A pattern alone does not tell what caused it.
When should I use direction of association?Scatterplots and Association: Describe how two measured quantities tend to change together.
What method supports association versus cause?Scatterplots and Association: association ≠ causation
Residual interpretationScatterplots and Association: Subtract the model from what actually happened.
Direction of associationScatterplots and Association: Positive rises together; negative moves in opposite directions.
What must I check in scatterplots and association?Scatterplots and Association: Association is a pattern, not proof of causation; strength and direction are separate features
What method supports residual interpretation?Scatterplots and Association: residual=y_observed−y_predicted
What method supports direction of association?Scatterplots and Association: direction is the sign of the trend
When should I use association versus cause?Scatterplots and Association: Recognize an observational limitation.
When should I use residual interpretation?Scatterplots and Association: Measure an observation relative to a fitted prediction.
Interpolation and extrapolationLines of Best Fit and Predictions: Inside the data range is interpolation; outside is extrapolation.
When should I use prediction from a fitted line?Lines of Best Fit and Predictions: Evaluate a model at a specified input.
What method supports interpolation and extrapolation?Lines of Best Fit and Predictions: x within observed [a,b]: interpolation
Interpret model slopeLines of Best Fit and Predictions: A fitted slope describes a predicted association per input unit.
Prediction from a fitted lineLines of Best Fit and Predictions: Use the model rule to estimate the output.
What must I check in lines of best fit and predictions?Lines of Best Fit and Predictions: Predictions are estimates; extrapolation beyond observed inputs can be unreliable
What method supports interpret model slope?Lines of Best Fit and Predictions: Δŷ=mΔx
What method supports prediction from a fitted line?Lines of Best Fit and Predictions: ŷ=mx+b
When should I use interpolation and extrapolation?Lines of Best Fit and Predictions: Classify a prediction relative to the observed input range.
When should I use interpret model slope?Lines of Best Fit and Predictions: Interpret a per-unit predicted change without assuming causation.
Second differencesComparing Linear, Quadratic, and Exponential Models: If the gains themselves change by the same amount, test a quadratic.
When should I use compare first differences?Comparing Linear, Quadratic, and Exponential Models: Identify a linear pattern in an equally spaced table.
What method supports second differences?Comparing Linear, Quadratic, and Exponential Models: unit-step second difference=2a
Compare constant ratiosComparing Linear, Quadratic, and Exponential Models: Repeated multiplication suggests an exponential rule.
Compare first differencesComparing Linear, Quadratic, and Exponential Models: Equal steps and equal gains suggest a line.
What must I check in comparing linear, quadratic, and exponential models?Comparing Linear, Quadratic, and Exponential Models: Fit describes observed patterns; several models can fit a small sample and none guarantees causality or distant forecasts
What method supports compare constant ratios?Comparing Linear, Quadratic, and Exponential Models: exponential: y_(t+1)/y_t=b
What method supports compare first differences?Comparing Linear, Quadratic, and Exponential Models: linear: constant first differences
When should I use second differences?Comparing Linear, Quadratic, and Exponential Models: Recognize a quadratic pattern with equally spaced inputs.
When should I use compare constant ratios?Comparing Linear, Quadratic, and Exponential Models: Identify multiplicative change in an equally spaced table.
Recover a missing cellTwo-Way Tables and Relative Frequencies: A total is the sum of its pieces.
When should I use joint relative frequency?Two-Way Tables and Relative Frequencies: Divide a cell by the grand total for a joint event.
What method supports recover a missing cell?Two-Way Tables and Relative Frequencies: missing cell=row total−known cell
Conditional row frequencyTwo-Way Tables and Relative Frequencies: Among a group means ignore everyone outside that group.
Joint relative frequencyTwo-Way Tables and Relative Frequencies: For both properties in the whole sample, use the cell over everyone.
What must I check in two-way tables and relative frequencies?Two-Way Tables and Relative Frequencies: Relative frequency uses the population specified in the question: whole table, row, or column
What method supports conditional row frequency?Two-Way Tables and Relative Frequencies: conditional frequency=overlap/condition-group total
What method supports joint relative frequency?Two-Way Tables and Relative Frequencies: joint frequency=cell/grand total
When should I use recover a missing cell?Two-Way Tables and Relative Frequencies: Use row and column totals to reconstruct a table.
When should I use conditional row frequency?Two-Way Tables and Relative Frequencies: Use the total of the condition group as the denominator.
Union and overlapProbability and Complementary Events: Add both groups, then remove the people counted twice.
When should I use simple event probability?Probability and Complementary Events: Count favorable and total equally likely outcomes.
What method supports union and overlap?Probability and Complementary Events: P(A or B)=P(A)+P(B)−P(A and B)
Complementary eventsProbability and Complementary Events: Sometimes it is easier to count what does not happen.
Simple event probabilityProbability and Complementary Events: Count the wins and divide by all possible draws.
What must I check in probability and complementary events?Probability and Complementary Events: Assume uniform selection only when the prompt states or implies each listed item is equally likely
What method supports complementary events?Probability and Complementary Events: P(not E)=1−P(E)
What method supports simple event probability?Probability and Complementary Events: P(E)=favorable/total
When should I use union and overlap?Probability and Complementary Events: Count either event without double-counting their intersection.
When should I use complementary events?Probability and Complementary Events: Use one minus a probability for the event not occurring.
Test independenceConditional Probability: Knowing B must not change the chance of A.
When should I use condition on a group?Conditional Probability: Compute a probability inside a specified subgroup.
What method supports test independence?Conditional Probability: independent ⇔ P(A|B)=P(A) when P(B)>0
Without-replacement probabilityConditional Probability: Remove the known first item before counting the next draw.
Condition on a groupConditional Probability: Given B means only B outcomes are still eligible.
What must I check in conditional probability?Conditional Probability: A conditional probability changes the reference population; independence must be established, not assumed
What method supports without-replacement probability?Conditional Probability: P(second red | first red)=(r−1)/(N−1)
What method supports condition on a group?Conditional Probability: P(A|B)=P(A∩B)/P(B), P(B)>0
When should I use test independence?Conditional Probability: Compare conditional and unconditional probabilities.
When should I use without-replacement probability?Conditional Probability: Update counts after a first selection.