Mathematical models are frequently employed to interpret experimental data.
Beyond being cost-effective and efficient, state two other advantages of using statistical models.
A chemist is studying the relationship between the concentration of a catalyst, x x\,x mmol/L, and the rate of a specific chemical reaction, y y\,y units, at a constant low temperature.
A random sample of 10 observations was recorded and is shown in the table below.
| Concentration (xxx) | 0.5 | 0.8 | 1.2 | 1.5 | 2.0 | 2.4 | 2.7 | 3.1 | 3.5 | 4.3 |
|---|---|---|---|---|---|---|---|---|---|---|
| Reaction Rate (yyy) | 12.4 | 15.1 | 18.2 | 22.0 | 25.8 | 29.4 | 33.1 | 38.5 | 42.0 | 51.5 |
[You may use: ∑x=22\sum x = 22∑x=22, ∑y=288\sum y = 288∑y=288, ∑x2=61.98\sum x^2 = 61.98∑x2=61.98, ∑xy=772.45\sum xy = 772.45∑xy=772.45, Sxx=13.58S_{xx} = 13.58Sxx=13.58]
Calculate the value of SxyS_{xy}Sxy for this dataset.
Determine the equation of the regression line of y y\,y on x x\,x in the form y=a+bxy = a + bxy=a+bx. Give the values of a a\,a and b b\,b to 3 significant figures.
Interpret the meaning of the constant b b\,b in the context of this study.
Use your model to estimate the reaction rate when the concentration of the catalyst is 3.0 mmol/L.
Comment on the reliability of using this specific regression model to predict the reaction rate in a high-temperature industrial environment.
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.