Final answer:
To determine if y is proportional to x, identify the independent and dependent variables, draw a scatter plot, calculate the least-squares line (checking if the y-intercept is near zero), and find the correlation coefficient to assess the strength of the relationship. Outliers and the fit of the line should also be considered.
Step-by-step explanation:
To determine if y is proportional to x, we need to follow several steps. Firstly, we identify the independent and dependent variables. Typically, the independent variable is the one we have control over or is stable, like time or age, while the dependent variable is what we measure or is affected by the independent variable.
Next, we draw a scatter plot of the data to visually check for a relationship between the variables. If the data points lie on or very close to a straight line that passes through the origin, this suggests that the variables might be directly proportional.
Afterwards, we calculate the least-squares line and put the equation in the form ý = a + bx. If the line fits well and a (the y-intercept) is zero or near zero, it indicates proportionality. The proportionality constant in a proportional relationship is represented by the slope b in the equation.
Furthermore, we compute the correlation coefficient to quantify the strength and direction of the relationship between the variables. A correlation coefficient close to +1 or -1 signifies a strong linear relationship.
It is also important to check for outliers and to consider if a line is the best way to fit the data, as these can affect the determination of proportionality. In some contexts, the slope and estimated values for specific data points can also provide insight about the relationship.