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

Linear regression and prediction Problem set B Answers

Skills

1. (a) y = −1.36x + 114
2. (b) y = 56.9
1. (a) Each 1 °C rise in the average temperature lowers the bill by €3.8, on average
2. (b) At an average temperature of 0 °C the bill is €145, on average. 0 °C is outside the range 2 to 24, so take care
1. (a) Q1 = 22.5, Q3 = 33.5; limits 6 and 50; y = 2 is an outlier
2. (b) Q1 = 5, Q3 = 12.5; limits −6.25 and 23.8; no outlier in x
1. (a) y = 85.4
2. (b) y = 207.5; extrapolation, so unreliable: growth rarely stays the same for 25 years beyond the data

1. (a) (18, 40)
2. (b) With: y = −3.27x + 124, r = −0.910. Without: y = −3.36x + 128, r = −0.996
3. (c) The gradient is −3.27 with the point and −3.36 without it, and |r| falls from 0.996 to 0.910: the point weakens the correlation
1. (a) Temperature falls quickly for the first 25 minutes then slowly: the points bend, so one line fits neither part
2. (b) 5 to 25 minutes: y = −2.54x + 92.3; 30 to 50 minutes: y = −0.4x + 36.2
3. (c) y = 49.1
1. (a) 23.5 minutes
2. (b) The line of y on x is for estimating time from distance, not distance from time. Also 54.8 km is outside the range of the data, so it is an extrapolation.

1. (a) y = −2.4x + 54, r = −0.999
2. (b) y = −1.35x + 45.5, r = −0.604
3. (c) The gradient changes from −2.4 to −1.35 and |r| falls from 0.999 to 0.604: the new point lies well above the trend, so it flattens the line and weakens the correlation
1. (a) When x = 0 the model gives 8.9 hours of sleep. 0 is outside the data range 1 to 8, so the value is not reliable
2. (b) x = 5: y = 7.15, inside the range, but |r| = 0.52 is only moderate, so the prediction is rough. x = 16: y = 3.3, outside the range, so unreliable

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