Chapter 12: Tests of Association: Correlation

[#1]

How do I understand this concept of statistics? Maybe my statistics is not enough :))))

[#2]

Hello @thiennguyen , please find bellow my understanding:

For the a given result of quantity x1, represented on the x-axis, there is a correspondent result of quantity x2, represented on the y-axis values.

The pictures shows that could be a trend, when the x1 value increases there might be a reduction on the x2 values, picturing a potential negative correlation (solid red line).

However, in some cases this negative trend might be not so strong, which drives uncertainty on the slope calculation. This uncertanty is represented by the confidence intervals (dashed red lines). Given the uncertainty, i.e. if new data is acquired, there are chances that the slope of the red line could assume any angle inside the confidence interval bounds and if the slope angle can assumes the value 0, the correlaction might not exist.

Graphically this can be seen in the picture if the green line (which is a line with slope angle of 0) is inside the confidence interval envelope. 

Hope it helps,

[#3 · Accepted solution]

Hi @thiennguyen,

Please find explanations of the different elements of this plot in the JMP Help related to Effect Leverage Plots.

In the bivariate plot you show, the fit linear line (red) has a slope significantly different from the mean line (green), as the confidence curves crosse the mean/horizontal line. So the effect of the related X variable (here IOP) is significantly different from 0 (null hypothesis, represented by mean line (green)).

From the JMP help section about leverage plot :

I hope this will help your understanding,