In the equation Ŷ = 12.6 X + 5
A) a difference of one unit in X will lead to a 5 point difference in the prediction.
B) Ŷ will decrease as X increases.
C) the correlation is certain to be significant.
D) a difference of one unit in X will lead to a 12.6 point difference in the prediction.

Question

In the equation Ŷ  = 12.6 X + 5
A) a difference of one unit in X will lead to a 5 point difference in the prediction.
B) Ŷ will decrease as X increases.
C) the correlation is certain to be significant.
D) a difference of one unit in X will lead to a 12.6 point difference in the prediction.

Quizplus · Accepted Answer

The coefficient of X, 12.6, represents the amount by which Ŷ changes for a one-unit change in X. Therefore, a difference of one unit in X will lead to a 12.6 point difference in the prediction. Option A is incorrect because the intercept of 5 represents the value of Ŷ when X is equal to 0, so a difference of one unit in X will not necessarily lead to a 5 point difference in the prediction. Option B is also incorrect because there is no information given about the direction of the relationship between X and Ŷ. Option C is also incorrect because the information given does not provide information about the correlation between X and Y.

In the Equation Ŷ = 12