From the regression equation, we can estimate the number of bears by:

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BlackTom AI · Accepted Answer

First, let’s restate what we’re analyzing: a regression equation is used to estimate the number of bears from the available predictor, which in this case is the number of humans in the area. We need to inspect each option to see how the regression output could be applied.
Option A says: Multiply the number of humans in the area by 5.71, and subtract that product from 4634.03. This structure resembles a linear model of the form Bears = Intercept - (Slope × Humans) if 4634.03 is the intercept and 5.71 is the coefficient with a negative sign, implying bears decrease as human count increases. If the original regression was designed with an intercept of 4634.03 and a coefficient of -5.71 on Humans, this option would match that model.
Option B says: Multiply the number of humans in the area by 5.71, and subtract the result from 306.0. Here the intercept would be 306.0 with the same positive slope magnitude, implying a different intercept than in the common regression form. Unless the regression explicitly stated that the intercept is 306.0 with a negative effect of humans, this option is inconsistent with a typical interpretation of a bears-from-humans regression.
Option C says: Multiply the number of humans in the area by 0.97, and subtract the result from 4634.03. This uses a slope of 0.97, not 5.71, which would indicate a much smaller effect of each additional human on the bear estimate. If the original regression coefficient for Humans is 5.71, this option misstates the slope and would yield incorrect estimates unless the actual coefficient were 0.97, which the prompt does not indicate.
Option D says: Multiply the number of bears in the area by 0.97, and add 306.04. This option reverses the predictor entirely by using Bears as the multiplier and adds a constant, which does not reflect a standard form for predicting bears from humans. It misinterprets the regression direction and the role of the intercept, making it unlikely to be correct given a regression of Bears on Humans.
Across the options, the critical distinction is the sign and the intercept/ slope pair that aligns with the regression equation form for predicting bears from humans. If the regression model is Bears = 4634.03 – 5.71 × Humans, Option A precisely matches that structure by subtracting 5.71 times Humans from 4634.03. Other options either use an incorrect intercept, an incorrect slope, or apply the wrong variables altogether, leading to logically inconsistent or numerically incompatible predictions.
In summary, Option A is the only choice that preserves the typical linear form Bears = Intercept – (Slope × Humans) with the given numbers, whereas Options B, C, and D introduce mismatched coefficients, intercepts, or predictor roles that do not align with the stated regression setup.

PSYC20009_2025_SM2 Lecture 3 Quiz

From the regression equation, we can estimate the number of bears by:

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