Beavers and beetles Do beavers benefit beetles? Researchers laid out $23$ circular plots, each $4$ meters in diameter, in an area where beavers were cutting down cottonwood trees. In each plot, they counted the number of stumps from trees cut by beavers and the number of clusters of beetle larvae. Ecologists think that the new sprouts from stumps are more tender than other cottonwood growth, so beetles prefer them. If so, more stumps should produce more beetle larvae. Here are the data:

A regression line is a straight line that depicts the change in a response variable $y$ when an explanatory variable $x$ changes. By putting this $x$ into the equation of the line, you may use a regression line to predict the value of $y$ for any value of $x$

The four-step approach can be used to determine whether the data support the stated notion or not:

(a). "What is the link between beetle larvae and stumps?" is the proper inquiry.

(b). The computation of the correlation and the regression line are valid statistical operations, and the regression line and correlation in this example are:

Thus, the correlation coefficient is $0.839$and the regression equation is$\stackrel{⏜}{y}=11.894x-1.286$

(c). The scatterplot could be constructed as:

(d). The scatter plot above demonstrates that the two variables have a strong positive association. The above explanation demonstrates that the evidence backs up the claim.