Final answer:
Linear regression is useful for predicting the value of a quantitative variable based on another quantitative variable, using a line of best fit like the least-squares regression line, especially when a strong correlation exists between the variables.
Step-by-step explanation:
Linear regression is indeed useful when you wish to predict the value of a quantitative variable based on another quantitative variable. This approach is particularly helpful when the data points show a linear trend, indicating a potential linear relationship between the two variables. Through the use of a scatter plot and the calculation of a line of best fit, typically the least-squares regression line, we can establish a predictive model. For example, if we know a student's score on a third exam (x), we can often predict their final exam score (y) by establishing a regression line that best fits the observed data points linking these two variables.
When a strong correlation coefficient is present, it can be indicative of a relevant predictive relationship between the variables. The least-squares regression line is calculated in a way that minimizes the residuals, which are the distances between the actual data points and the estimated values predicted by the regression line. While this technique is powerful for making predictions within the range of existing data, it may not be suitable for extrapolating predictions outside of this range.
Therefore, it is true that linear regression can be used to predict the value of one quantitative variable based on another. However, it is also important to test the significance of the correlation coefficient to ensure that the regression model provides a meaningful prediction.