An environmental scientist is investigating the effect of daily light intensity, LLL lux, on the vertical growth rate of a specific type of algae, GGG mm/day, in a controlled lab environment. Over a period of 12 days, the following summary statistics were recorded:
∑L=600,∑L2=32800,∑G=156,SGG=450 \sum L = 600, \quad \sum L^2 = 32800, \quad \sum G = 156, \quad S_{GG} = 450 ∑L=600,∑L2=32800,∑G=156,SGG=450Calculate the value of SLLS_{LL}SLL.
The scientist calculated the product moment correlation coefficient between LLL and GGG to be 0.925, correct to 3 decimal places.
State, giving a reason, whether or not this correlation coefficient supports the use of a linear regression model to describe the relationship.
State, giving a reason, why light intensity would be the explanatory variable.
Find the value of SLGS_{LG}SLG.
Calculate a suitable linear regression equation to model the relationship between growth rate and light intensity.
Calculate the standard deviation of LLL.
The scientist uses this model to estimate the growth rate on a day where the light intensity is 95 lux.
State the value of the scientist’s estimate for GGG.
Given that the values of LLL in the sample are all within 2.5 standard deviations of the mean,
comment, giving your reason, on the reliability of this estimate.
