A marine biologist is investigating the relationship between the time a coral specimen has been submerged in a controlled nursery and its total vertical height. She monitors a random sample of 30 specimens and records the time submerged, ttt months, and the vertical height, hhh cm.
The data were coded using x=t−104x = \frac{t - 10}{4}x=4t−10 and y=h5y = \frac{h}{5}y=5h and the following statistics were obtained:
∑x=150,∑y=360,∑x2=1150,∑y2=4670,∑xy=2080 \sum x = 150, \quad \sum y = 360, \quad \sum x^2 = 1150, \quad \sum y^2 = 4670, \quad \sum xy = 2080 ∑x=150,∑y=360,∑x2=1150,∑y2=4670,∑xy=2080Find the value of SxyS_{xy}Sxy and the value of SxxS_{xx}Sxx.
Find the equation of the least squares regression line of yyy on xxx in the form y=α+βxy = \alpha + \beta xy=α+βx.
The least squares regression line of hhh on ttt is h=k+mth = k + mth=k+mt.
Show that m=0.875m = 0.875m=0.875 and find the value of kkk.
Estimate the vertical height of a coral specimen that has been submerged for 24 months.
Interpret the value of mmm in context.
The biologist intends to leave a specimen submerged for an additional 8 months. Estimate the total increase in vertical height for this period based on the model.
278 exam-style questions on CCEA A Level Maths 2.5 Data presentation and interpretation, covering 2.5.1 Data presentation and interpretation, 2.5.2 Data presentation and interpretation, 2.5.3 Data presentation and interpretation, 2.5.4 Data presentation and interpretation, 2.5.5 Data presentation and interpretation, 2.5.6 Data presentation and interpretation, 2.5.7 Data presentation and interpretation, 2.5.8 Data presentation and interpretation, 2.5.9 Data presentation and interpretation, and 2.5 Data presentation and interpretation. Each one has a worked solution and a mark scheme showing where the marks go.