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Flashcards · 0479 · Topic 11

Bivariate distributions flashcards

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Topic 11: Bivariate distributions

Which variable goes on which axis of a scatter diagram?
The independent variable (the one you choose, control or predict from) on the x-axis; the dependent variable (the one that responds) on the y-axis.
How do you describe correlation fully?
Give the direction (positive or negative), the strength (strong or weak) and the context, for example "strong negative correlation: older laptops tend to be worth less".
What is the difference between strong, weak and no correlation?
Strong: points close to a straight line. Weak: points spread loosely but still showing a trend. None: no pattern at all.
How should a line of best fit be drawn by eye?
One straight ruled line through the middle of the points, following the trend, with similar numbers of points either side, across the range of the data. It need not pass through the origin.
How do you draw a line of best fit by semi-averages?
Sort the pairs by x, split them into a lower half and an upper half of equal size, find the mean point (mean x, mean y) of each half, then plot both mean points and join them.
Find the semi-average line for (2, 10), (4, 14), (6, 19), (8, 25)
Mean points (3, 12) and (7, 22). Gradient = (22 − 12) ÷ (7 − 3) = 2.5. Then 12 = 2.5 × 3 + c, so c = 4.5. y = 2.5x + 4.5.
In y = mx + c for a line of best fit, what do m and c mean?
m is the change in y for each one-unit increase in x. c is the value of y when x = 0, which may lie outside the data.
How do you estimate x from a given y using y = mx + c?
Rearrange to x = (y − c) ÷ m. Example: y = 2x + 6 and y = 40 → x = 34 ÷ 2 = 17.
What is the difference between interpolation and extrapolation?
Interpolation estimates inside the range of the data and is more reliable. Extrapolation estimates outside it and is less reliable, because the pattern may not continue.
What assumptions lie behind an estimate from a line of best fit?
The straight-line trend continues for the values used, the sample is representative, and other influences stay the same. Correlation by itself does not show that one variable causes the other.

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