Final answer:
To determine a relationship in a scatterplot, identify the independent and dependent variables, draw the scatter plot, look for patterns, calculate the line of best fit, and then find the correlation coefficient to measure the strength of the relationship.
Step-by-step explanation:
To identify a relationship in a scatterplot, you should first distinguish which variable is the independent variable, which is typically plotted on the x-axis, and the dependent variable, plotted on the y-axis. Then, draw the scatter plot with the data points. You'll look for patterns that suggest a relationship; this could be a positive correlation, where one variable increases as the other does, or a negative correlation, where one variable decreases as the other increases. Next, calculate the least-squares line or the line of best fit and put the equation in the form ý = a + bx. Finally, find the correlation coefficient to quantitatively measure the strength and direction of the relationship. If the correlation coefficient is close to +1 or -1, it suggests a strong positive or negative linear relationship, respectively. However, if it is close to 0, there may be no linear relationship. It's essential to examine the scatter plot to determine if a linear model is applicable or if a curve would better fit the data.