QuestionGiven the weight prediction formula , which statements are true? A. I only B. II and III only C. I and II only D. III only E. II only. Select one.
Studdy Solution
STEP 1
Assumptions1. The regression equation for predicting weight from height is given by Weight = -115 +3.6 * Height. The height is measured in inches and the weight is measured in pounds.
STEP 2
Let's evaluate each statement one by one.
Statement I A person who is61 inches tall will weigh104.6 pounds.
We can verify this by substituting the height (61 inches) into the regression equation and calculating the predicted weight.
STEP 3
Substitute the height value into the equation.
STEP 4
Calculate the predicted weight.
So, statement I is correct.
STEP 5
Statement II For every additional inch of height, the predicted weight will increase, on average, by3. pounds.
This statement is referring to the slope of the regression line, which is3.. This means that for every increase of1 in the height (in inches), the predicted weight (in pounds) increases by3.. So, statement II is also correct.
STEP 6
Statement III The correlation between weight and height is negative.
The correlation between two variables in a linear regression is indicated by the sign of the slope. In this case, the slope is positive (3.6), which means that as height increases, weight also increases. Therefore, the correlation is positive, not negative. So, statement III is incorrect.
STEP 7
Based on the evaluations, statements I and II are correct, while statement III is incorrect. Therefore, the correct answer is C. I and II only.
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