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Two-Variable Data: Models and Scatterplots
I worked these out from the practice questions. Each code says where to start reading, where to stop, what you can skip, and why it is safe.
1. Plug in, do not think
- Start:
- The x-value in the question and the equation.
- Stop:
- When you have a number for y.
- Skip:
- The story around the equation until you need units.
- Why:
- Prediction questions are only substitution, and the calculator does it without errors.
Used in questions 1, 5
2. Slope and intercept in words
- Start:
- The equation, then the two units given for x and y.
- Stop:
- When you can say 'for each extra [x unit], y changes by [slope]'.
- Skip:
- Options that say the 'start' value is the slope.
- Why:
- The slope is always per one unit of x, and the intercept is the value at x = 0.
Used in questions 2, 7
3. Test the options with two points
- Start:
- Two data points from the table, far apart.
- Stop:
- When only one option fits both.
- Skip:
- Computing a full regression by hand.
- Why:
- Wrong options usually fail on the sign or the size, so two checks are enough.
Used in question 3
4. Residual = actual − predicted
- Start:
- The given model and the point's x-value.
- Stop:
- When you have predicted and actual side by side.
- Skip:
- The other points when the question only asks about one.
- Why:
- The residual is a simple subtraction. For 'which point', do all points and look at the biggest size.
Used in questions 4, 6
5. Check equal differences or equal ratios
- Start:
- The y-values in a table or the model's form.
- Stop:
- When you know if y changes by adding or by multiplying.
- Skip:
- Fitting a line to an exponential pattern.
- Why:
- Adding the same amount means linear; multiplying by the same factor means exponential.
Used in questions 5, 8
6. Watch the units
- Start:
- The unit of x and the unit asked (days, weeks, years).
- Stop:
- After you convert the slope to the unit asked.
- Skip:
- Using the per-day slope as the per-week answer.
- Why:
- The SAT often asks for a different time unit than the one in the data; multiply the slope by the number of days in a week.
Used in question 7
7. Desmos table
- Start:
- Type the points into a Desmos table and type y1 ~ mx1 + b.
- Stop:
- When Desmos shows the best-fit values.
- Skip:
- Doing sums for the slope by hand.
- Why:
- Desmos finds the line of best fit instantly, and you can compare it with the options.
Used in question 3
8. Line gives predicted, dot gives actual
- Start:
- The words 'predicted', 'according to the line' or 'the model'.
- Stop:
- When you have put the x-value into the equation, not read the dot.
- Skip:
- The real data in the table for that x. It is the usual wrong option.
- Why:
- Predicted values come only from the equation. The actual value is the dot, and the residual is the gap between them.
Used in questions 9, 14
9. Match the exponent to the time step
- Start:
- The table: how long it takes for the value to double, halve or be multiplied by 1.5.
- Stop:
- When you can write the exponent as t divided by that time step.
- Skip:
- Using t alone in the exponent when the step is not 1.
- Why:
- If the amount changes every 2 hours, the exponent must count 2-hour periods. Testing two table rows proves it.
Used in questions 13, 15
10. Two points on the line, then slope, then intercept
- Start:
- Two points that the line passes through, from the figure or the sentence.
- Stop:
- When you have slope = rise ÷ run and b from y = mx + b.
- Skip:
- A y-value as the intercept. Only the value at x = 0 is the intercept.
- Why:
- Any two points fix a line. Then you can check the equation by putting in the second point.
Used in question 12
11. Quadratic: go to the vertex
- Start:
- The words 'maximum', 'minimum' or 'highest point'.
- Stop:
- When you have found t = −b ÷ 2a and put it back in.
- Skip:
- The largest number in the table. The true peak can fall between table rows.
- Why:
- The extreme value of a quadratic is at the vertex, and the table may not contain that exact x.
Used in question 16