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IB Mathematics: Applications and Interpretation SL · 13.3: Statistics · 13.3.7

Linear regression and prediction Problem set A Answers

Skills

    1. (a) y = 2.45x + 6.27
    2. (b) y = 30.8
    1. (a) Each extra kilometre adds €1.9 to the fare, on average
    2. (b) A journey of 0 km would cost €4.5 on average: a fixed charge. 0 km is outside the range 2 to 25, so take care
    1. (a) Q1 = 46, Q3 = 61; limits 23.5 and 83.5; y = 95 is an outlier
    2. (b) Q1 = 16, Q3 = 24; limits 4 and 36; no outlier in x
    1. (a) y = 108
    2. (b) y = 396; extrapolation, so unreliable: a sunflower stops growing

In context

    1. (a) (8, 35)
    2. (b) With: y = 3.69x + 26.6, r = 0.913. Without: y = 3.57x + 30.1, r = 0.996
    3. (c) The gradient is 3.69 with the point and 3.57 without it, and |r| falls from 0.996 to 0.913: the point weakens the correlation
    1. (a) Speed rises quickly in weeks 1 to 5 then slowly: the points bend, so one line fits neither part
    2. (b) Weeks 1 to 5: y = 3.3x − 0.3; Weeks 6 to 10: y = 1.2x + 9.4
    3. (c) y = 19.6
    1. (a) €516
    2. (b) The line of y on x is for estimating sales from temperature, not temperature from sales. Also 31.4 °C is outside the range of the data, so it is an extrapolation.

Stretch

    1. (a) y = 3.08x + 8.75, r = 0.997
    2. (b) y = 1.65x + 13.5, r = 0.600
    3. (c) The gradient changes from 3.08 to 1.65 and |r| falls from 0.997 to 0.600: the new point lies well below the trend, so it flattens the line and weakens the correlation
    1. (a) When x = 0 the model gives 78 beats per minute. 0 is outside the data range 1 to 9, so the value is not reliable
    2. (b) x = 6: y = 67.8, inside the range, but |r| = 0.46 is only weak, so the prediction is rough. x = 20: y = 44, outside the range, so unreliable (and a very low heart rate)

jmaths.xyz · AI SL · 13.3.7 Linear regression and prediction