A researcher investigates the relationship between the number of charge cycles, nnn, and the maximum flight duration, ddd minutes, of a drone's battery. A random sample of 30 batteries is analyzed and the results are recorded.
The data were coded using x=n−405x = \frac{n - 40}{5}x=5n−40 and y=d−102y = \frac{d - 10}{2}y=2d−10 and the following summary statistics were obtained:
∑x=60,∑y=150,∑x2=380,∑y2=900,∑xy=180 \sum x = 60, \quad \sum y = 150, \quad \sum x^2 = 380, \quad \sum y^2 = 900, \quad \sum xy = 180 ∑x=60,∑y=150,∑x2=380,∑y2=900,∑xy=180Calculate the values of SxyS_{xy}Sxy and 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 ddd on nnn is given by d=k+mnd = k + mnd=k+mn.
Show that m=−0.185m = -0.185m=−0.185 to 3 significant figures and find the value of kkk.
Estimate the flight duration of a battery that has undergone 100 charge cycles.
Interpret the value of mmm in the context of this study.
The researcher plans to use a battery for an additional 25 charge cycles beyond its current usage. Estimate the change in flight duration 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.