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Using illustrations on the regression equation: Y = a + bX +e, where Y is the value of the Dependent variable (Y), and what is being predicted or explained. a or Alpha, is a constant; equals the value of Y when the value of X=0. b or Beta, the coefficient of X; the slope of the regression line; how much Y changes for each one-unit change.

a. Estimate the value of Y.

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The estimated value of the dependent variable (Y) is given by the regression equation Y=a+bX+e, where a is the constant (intercept) and b is the coefficient of X (slope).

In the regression equation Y=a+bX+e, where Y represents the dependent variable being predicted or explained, a is the constant (also known as the intercept), and b is the coefficient of X (the independent variable). The constant a signifies the value of Y when X is equal to 0. In practical terms, it represents the starting point of the regression line on the

Y-axis. On the other hand, the coefficient b indicates the slope of the regression line, illustrating how much Y changes for each one-unit change in X. Therefore, when estimating the value of Y using this regression equation, one considers both the constant a and the coefficient b in relation to the specific value of X in question. This formula serves as a valuable tool in predicting or explaining Y based on the relationship with the independent variable X in a given dataset.

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