Final answer:
Joe can create a scatterplot, perform correlation analysis, and conduct regression analysis including calculating the least-squares line and correlation coefficient to understand the relationship between rock sample densities.
Step-by-step explanation:
When Joe has worked out the density of each piece of rock, to find out if there is a relationship between the rock samples and their density, he can do all of the following:
- Create a scatterplot to visualize the data, deciding which variable should be the independent variable and which should be the dependent variable.
- Perform a correlation analysis to measure the strength and significance of the relationship.
- Conduct a regression analysis to determine if there is a significant linear relationship, which includes calculating the least-squares line and putting the equation in the form ý = a + bx.
The correlation coefficient resulting from the correlation analysis will indicate the degree to which the variables are linearly related. Furthermore, by creating a scatterplot and drawing the least-squares line, he can visually inspect the data for a linear relationship. These statistical methods will help Joe understand the nature of the relationship between density and the characteristics of the rock samples.