In the regression equation, Y=75.65+0.50X, the intercept isa.0.5b.75.65c.1d.Undeterminable

Break Down the Problem

1. Identify the components of the regression equation.
2. Determine the value of the intercept based on the regression form.

Relevant Concepts

The general form of a linear regression equation is given by: $Y = a + bX$ where:

• $a$ is the intercept,
• $b$ is the slope of the line.

Analysis and Detail

1. In the equation $Y = 75.65 + 0.50X$:

   • $75.65$ is the constant term added to the product of the slope and $X$.
   • The slope $b = 0.50$ represents the change in $Y$ for a one-unit change in $X$.

2. The intercept is the value of $Y$ when $X = 0$, which in this case is $75.65$.

Verify and Summarize

Since the constant term is identifiable in the equation, the intercept can be directly confirmed from the regression equation provided.

Final Answer

The intercept is b. 75.65.