A climatologist investigates the relationship between the concentration of a specific atmospheric pollutant, xxx mg/m3^33, and the annual growth rate of a certain species of alpine lichen, yyy mm/year, for a random sample of 30 lichen specimens.
The following summary statistics were recorded:
Sxy=−216Sxx=480∑y=180∑x=450∑y2=1205.2 S_{xy} = -216 \quad S_{xx} = 480 \quad \sum y = 180 \quad \sum x = 450 \quad \sum y^2 = 1205.2 Sxy=−216Sxx=480∑y=180∑x=450∑y2=1205.2Show that the product moment correlation coefficient (PMCC) for these data is −0.881-0.881−0.881 to 3 significant figures.
A scatter diagram of yyy against xxx is drawn. State two features of the scatter diagram you would expect to see based on the PMCC value.
Calculate the equation of the regression line of yyy on xxx in the form y=a+bxy = a + bxy=a+bx. Give the values of aaa and bbb to 3 significant figures.
Interpret the value of the gradient of this regression line within the context of the study.
The climatologist decides to convert the pollutant concentration from milligrams per cubic metre (mg/m3^33) to grams per cubic metre (g/m3^33) by dividing all xxx values by 1000.
State, for each of the following, whether the value would increase, decrease, or stay the same as a result of this change: (i) the product moment correlation coefficient, (ii) the magnitude of the gradient of the regression line, (iii) the yyy-intercept of the regression line.
