Below are the results from two different trees. Tree 71 Dependent Variable: Tree

Question

Below are the results from two different trees. Tree 71 Dependent Variable: Tree 71 leaf water potential Independent Variable: Tree 71 sap flow velocity Tree 71 W leaf water potential--0.64752549 0.019707641 Tree 71 sap flow velocity Sample size: 6 R (correlation coefficient)- -0.95677727 R-sq 0.91542275 Estimate of error standard deviation: 0.11710163 Tree 71 ? leaf water potential 0.8t Legend Fitted line 1.6 10 20 30 40 50 Tree 71 sap flow velocity Tree 68 Simple linear regression results Dependent Variable: Tree 68 leaf water potential Independent Variable: Tree 68 sap flow velocity Tree 68 leaf water potential -0.68469882 -0.036908582 Tree 68 sap flow velocity

Explanation / Answer

We are given the results of 2 different trees where simple linear regression to the data is applied.

For tree 71 :-

     The fitted simple linear regression is :

                 Tree 71 leaf water potential = -0.64752549 - 0.019707641 Tree 71 sap flow velocity

                 Sample correlation = -0.95677727

For tree 68 :-

                 The fitted simple linear regression is :

                 Tree 68 leaf water potential = -0.68469882 - 0.036908582 Tree 68 sap flow velocity

                 Sample correlation = -0.8429893

Note that correlation is a measure of association of linear relationship between two variables under study. It varies between -1 and +1. Zero correlation implies that there is no form of linear relation between the variables.

     Comparing the value of correlation in both cases ,clearly tree 71 shows stronger correlation.

Now, any linear equation is represented as :

                                           y = mx +c

                                       where c is the intercept on y axis

                                                 m is the slope of the line determining the inclination with the x axis

Here comparing the slopes of the 2 regression equations, the absolute value of the slope of tree 68 is greater than that of tree 71 and thus is more steeper.

Therefore combining the 2 findings, option 2 is correct.

                Tree 71 has a stronger correlation and a less steep slope than tree 68.

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