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.
