What is a scatterplot?

What algebraic concept is used to determine the type of correlation in a scatterplot?

A botanist records the amount of fertilizer in grams used and the resulting height in centimeters of tomato plants after two months. The data and the corresponding scatterplot are as follows:

Calculate the value of the linear correlation coefficient $r$ and determine the critical values of $r$ at a significance level of $\alpha =0.05$. Is there enough evidence to support a claim that there is a linear correlation between the amount of fertilizer and plant height?

The following table lists battery life (in hours of continuous usage) and prices (in US dollars) for different smartphone models.

Use the rank correlation coefficient (Spearman’s $\rho$) to test the hypothesis of a correlation between battery life and price. Use $\alpha =0.05$. What conclusion can you draw?