What are the two events that are compared in the second and third
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The picture of how the graph looks like is shown in the picture.
Part A. The correlation coefficient, R², is the quantitative evaluation of how the data points are well-fitted to a model. The closer it is to 1, the better. But a R²=1 is very ideal and rare. This can be only true if the points coincides exactly with the given model. Since we can see in the graph that the points are exaclty passed through by the linear model, the correlation coefficient is 1.
Part B. The slope of the graph is measured between two points as Δy/Δx. So, between 1 to 4 hours, the slope is: (85-100)/(4-1) = -5. The slope represents the instantaneous rate of change of surface area with time. It is called instantaneous because the change was only between than interval, not the whole set of data. Also, the negative sign signifies that the trend is decreasing.
Part C. The data represents causation if the time was the cause of the change of the pond's surface area. However, this is not technically true because there might be other factors to be considered like environmental conditions. But, definitely, these data are in correlation because together they show an observable trend.
Part A. The correlation coefficient, R², is the quantitative evaluation of how the data points are well-fitted to a model. The closer it is to 1, the better. But a R²=1 is very ideal and rare. This can be only true if the points coincides exactly with the given model. Since we can see in the graph that the points are exaclty passed through by the linear model, the correlation coefficient is 1.
Part B. The slope of the graph is measured between two points as Δy/Δx. So, between 1 to 4 hours, the slope is: (85-100)/(4-1) = -5. The slope represents the instantaneous rate of change of surface area with time. It is called instantaneous because the change was only between than interval, not the whole set of data. Also, the negative sign signifies that the trend is decreasing.
Part C. The data represents causation if the time was the cause of the change of the pond's surface area. However, this is not technically true because there might be other factors to be considered like environmental conditions. But, definitely, these data are in correlation because together they show an observable trend.