Given a linear regression equation of the form $y=a+bx$ with $b=3$ and $a=-6$, what is the predicted value of $y$ when $x=4$?

• A. $18$
• B. $6$
• C. $-6$
• D. $9$

Answer: (B)

Verified step by step guidance

1. Identify the given linear regression equation in the form \(y = a + b x\), where \(a\) is the intercept and \(b\) is the slope.
2. Substitute the given values for the intercept and slope into the equation: \(a = -6\) and \(b = 3\), so the equation becomes \(y = -6 + 3x\).
3. Plug in the given value of \(x = 4\) into the equation to find the predicted value of \(y\).
4. Calculate the expression \(y = -6 + 3 \times 4\) by performing the multiplication first, then the addition.
5. The result from the calculation will give the predicted value of \(y\) when \(x = 4\).