What is the general form of the regression equation?
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A. B. C. D. E.Explanation
The regression is written as Y' = a + bX. The letter "a" is the Y intercept and b is the slope of the line.
The general form of a regression equation is expressed as:
Y' = a + bX
In this equation, Y' represents the predicted or estimated value of the dependent variable (Y). It is usually referred to as the "Y-hat" symbol. X represents the independent variable, and it is used to predict the value of the dependent variable.
The regression equation consists of two components: the intercept (a) and the slope (b). The intercept (a) is the value of Y when X is equal to zero, and it represents the starting point of the regression line. The slope (b) indicates the change in Y for a one-unit change in X. It determines the steepness or direction of the regression line.
Option C, Y' = a + bX, correctly represents the general form of the regression equation. Option A, Y' = a x bX, incorrectly includes multiplication between a and bX. Option B, Y' = a - bX, incorrectly subtracts bX from the intercept. Option D, Y' = ab, incorrectly multiplies a and b without including X. Finally, Option E states that none of the answers are correct, which is inaccurate since Option C is indeed the correct answer.
Therefore, the correct answer to the question is Option C, Y' = a + bX.