SAT Math
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.
