Question at position 33 CADEB

Question

BlackTom AI · Accepted Answer

The question presents a regression context and asks which statement is false. We will examine each option carefully, computing predictions or interpreting the model where needed.
Option A: It claims the model would predict 1.64 inches higher than da Vinci’s projection for a 62-inch tall student. Using the regression y = 11.5474 + 0.84024 × Height, for Height = 62, the prediction is 11.5474 + 0.84024×62 ≈ 11.5474 + 52.09488 ≈ 63.64228 inches. If the da Vinci projection is that armspan equals height (62 inches), then the predicted armspan is about 63.64 inches, which is 1.64 inches higher than 62. Thus this statement is true, not false.
Option B: It states the residual for a student with height 70.5 inches and armspan 68 inches would be −2.78 inches. Predicted y for 70.5 is 11.5474 + 0.84024×70.5 ≈ 11.5474 + 59.23692 ≈ 70.78432. The residual (observed − predicted) is 68 − 70.78432 ≈ −2.78432 inches, about −2.78. This matches the calculation, so this statement is true.
Option C: It claims the least-squares regression line has a steeper slope than the equation for da Vinci’s relationship between armspan and height. The regression slope here is 0.84024, which is less than 1.0, whereas da Vinci’s hypothetical relationship (armspan equals height) would have slope 1.0. Therefore the statement that it is steeper is incorrect; this is the false option.
Option D: It says for every one-inch increase in height, the model predicts about a 0.84-inch increase in armspan. The slope is 0.84024, which indeed corresponds to approximately 0.84 inches of armspan per extra inch of height. This is true.
Option E: It asserts that for a student 66 inches tall, the model would predict an armspan of about 67 inches. Compute: 11.5474 + 0.84024×66 ≈ 11.5474 + 55.45584 ≈ 67.00324 inches, which is about 67 inches. This is true.

Question at position 33 CADEB

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