Final answer:
The y-intercept in the regression equation y = 75.65 + 0.50x is 75.65.optin B is correct .
Step-by-step explanation:
In the regression equation y = 75.65 + 0.50x, the intercept is a point where the line crosses the y-axis, which occurs when the independent variable 'x' is zero. Based on the structure of linear equations, which can be written as y = a + bx, where 'b' represents the slope and 'a' represents the y-intercept, it is clear that the coefficient before 'x' is the slope and the constant term is the y-intercept. Therefore, the y-intercept in the given equation is 75.65.
In the regression equation
�
=
75.65
+
0.50
�
y=75.65+0.50x, the intercept is represented by the constant term, which is 75.65 in this case. The intercept is the point where the regression line intersects the y-axis when the independent variable (
�
x) is zero. In practical terms, it signifies the expected value of the dependent variable (
�
y) when the independent variable is absent or has a value of zero.
In the context of the provided equation, if
�
x were zero, the predicted value of
�
y would be 75.65. This intercept is crucial for interpreting the baseline value of the dependent variable and understanding how it changes as the independent variable varies. The slope of the regression equation, represented by 0.50 in this case, indicates the rate of change in
�
y for each one-unit increase in
�
x. Together, the intercept and slope contribute to defining the relationship between the variables in the regression model.