Question

a digital camera was used to photograph the moons orbit. the photos were used to measure the angular size, in pixels (p), of the moon at various heights above the horizon, measured in degrees (d). the data is illustrated in the graph below for 11 different heights, and it is modeled by a second - degree polynomial function with a coefficient of determination of 0.69. can this model be used to predict the angular size of the moon when it is 133 degrees above the horizon? this model can be used for this prediction since the model is moderately correlated, and the angular size at 133 degrees would be considered a safe extrapolation. this model can be used for this prediction since the model is strongly correlated, and the angular size at 133 degrees would be considered a safe extrapolation. this model cannot be used for this prediction since the model is moderately correlated, and the angular size at 133 degrees would be considered an extreme extrapolation. this model cannot be used for this prediction since the model is moderately correlated, and the data would be better modeled with a linear function.

Explanation:

The coefficient of determination ($r^{2}=0.69$) indicates a moderate correlation. Also, 133 degrees is far beyond the range of the data (11 different heights shown on the graph), which is extreme extrapolation. Extrapolating far - outside the range of the data is unreliable even for moderately - correlated models.

Answer:

This model cannot be used for this prediction since the model is moderately correlated, and the angular size at 133 degrees would be considered an extreme extrapolation.