Question

listed below are the overhead widths (cm) of seals measured from photographs and weights (kg) of the seals. find the regression equation, letting the overhead width be the predictor (x) variable. find the best predicted weight of a seal if the overhead width measured from a photograph is 2.3 cm, using the regression equation. can the prediction be correct? if not, what is wrong? use a significance level of 0.05.\
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overhead width (cm) | 7.2 | 7.4 | 9.8 | 9.3 | 8.7 | 8.4\
weight (kg) | 121 | 159 | 252 | 205 | 203 | 196\
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can the prediction be correct? if not, what is wrong?\
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a. the prediction cannot be correct because there is not sufficient evidence of a linear correlation. the width in this case is beyond the scope of the available sample data.\
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b. the prediction cannot be correct because a weight of zero does not make sense and because there is not sufficient evidence of a linear correlation.\
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c. the prediction cannot be correct because a negative weight does not make sense. the width in this case is beyond the scope of the available sample data.\
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d. the prediction can be correct.

Explanation:

First, we check the sample data for overhead widths (x: 7.2, 7.4, 9.8, 9.3, 8.7, 8.4) and weights (y). The given x - value for prediction is 2.3 cm, which is much lower than all sample x - values (the minimum sample x is 7.2 cm). Also, we need to check linear correlation. If there's not enough evidence of linear correlation, and the x - value is outside the sample's x - range (extrapolation), the prediction is unreliable. Option A states that the prediction can't be correct because there's not sufficient evidence of linear correlation and the width is beyond the sample data's scope, which matches the situation. Option B's "weight of zero" is not relevant here. Option C's "negative weight" isn't indicated. Option D is wrong as the prediction has issues.

Answer:

A. The prediction cannot be correct because there is not sufficient evidence of a linear correlation. The width in this case is beyond the scope of the available sample data.