Final answer:
When selecting important variables in a data set, follow these steps: decide on the independent and dependent variables, draw a scatter plot, inspect for relationships, calculate the least-squares line, find the correlation coefficient, estimate values, and consider line fit.
Step-by-step explanation:
When selecting important variables in a data set, there are several steps to follow:
- Decide which variable should be the independent variable and which should be the dependent variable.
- Draw a scatter plot of the data to visualize any potential relationships between the variables.
- Inspect the scatter plot to determine if there is a relationship between the variables. Look for patterns such as a linear or non-linear trend.
- Calculate the least-squares line, which represents the best fit line for the data points. The equation of the line is in the form ŷ = a + bx, where ŷ is the predicted value, a is the intercept, b is the slope, and x is the independent variable.
- Find the correlation coefficient, which measures the strength and direction of the relationship between the variables. A correlation coefficient close to 1 or -1 indicates a strong relationship.
- Estimate the average height for specific age groups using the least-squares line and the independent variable values.
- Finally, consider if a linear line is the best way to fit the data based on the scatter plot and the correlation coefficient. A non-linear relationship may require a different approach.