Final answer:
The regression equation used to predict the value of the dependent variable based on the independent variable is in the form îy = a + bx, where a represents the y-intercept and b is the slope of the line. This equation derives from methods like least-squares regression, which computes the line of best fit by minimizing prediction errors.
Step-by-step explanation:
To predict the value of the dependent variable based on the independent variable, one would use a regression equation, often in the form of îy = a + bx. This equation is the result of a statistical method, such as the least-squares regression line, that determines the line of best fit by minimizing the differences between the observed values and the values predicted by the line. For a specific example, given in the scenario where the third exam score, x, is the independent variable and the final exam score, y, is the dependent variable, the regression line provided by the equation îy = -173.51 + 4.83x can be used to predict the final exam score based on the third exam score.
However, it's important to recognize the limitations of using this line for prediction. If a value of x is outside the domain of the observed data, the prediction may not be reliable. For instance, substituting x = 90 in the equation provided earlier yields a predicted y value of 261.19, but this prediction is unreliable as 90 is beyond the domain of the observed x values.