2. Both interpolated and extrapolated predictions are reliable methods of making predictions because ____.
A. they are supported by the research problem and hypothesis
B. they follow patterns and trends of the actual measurements
C. they are based on cause and effect relationship of variables
D. they have simple mathematical formulas as basis
The correct answer is B. Both interpolated and extrapolated predictions are reliable methods of making predictions because they follow patterns and trends of the actual measurements.
To understand why this answer is correct, let's break down the options:
A. "They are supported by the research problem and hypothesis" - This option suggests that the reliability of interpolated and extrapolated predictions depends on their alignment with the research problem and hypothesis. However, while this alignment can improve the validity of the predictions, it does not inherently make them reliable. Therefore, option A is not the correct answer.
B. "They follow patterns and trends of the actual measurements" - This option recognizes that reliable predictions are based on the patterns and trends observed in the actual measurements. Interpolation involves making predictions within the range of observed data, while extrapolation extends predictions beyond that range. When patterns and trends are consistently observed within the available data, it is reasonable to assume that they will continue to hold true beyond the observed range. Therefore, option B is the correct answer.
C. "They are based on cause and effect relationship of variables" - This option suggests that the reliability of interpolated and extrapolated predictions stems from their basis in cause and effect relationships between variables. While cause and effect relationships can certainly enhance the reliability of predictions, this is not the sole determining factor. Therefore, option C is not the correct answer.
D. "They have simple mathematical formulas as the basis" - This option implies that the simplicity of the mathematical formulas underlying interpolated and extrapolated predictions makes them reliable. However, the reliability of predictions does not solely depend on the simplicity of the formulas, but rather on their ability to capture and replicate the patterns and trends observed in the data. Therefore, option D is not the correct answer.
In summary, the most accurate answer is B - interpolated and extrapolated predictions are reliable because they follow patterns and trends evident in the actual measurements.