In simple linear regression, which expression represents the relationship?

In simple linear regression, which expression represents the relationship?

• A. y = b x + a
• B. y = a + b x^2
• C. y = a x + b
• D. y = b + a x

Answer: (A)

A straight-line relationship expresses y as a constant plus a term proportional to x. In simple linear regression, the model is y = intercept + slope × x. This means y changes by the slope amount for each unit change in x, and when x is zero, y is at the intercept level. The form y = b x + a matches that idea, with a as the intercept and b as the slope. It’s the same relationship as y = a + b x, just written with the terms swapped. This is why it’s the best representation here. The squared term would imply a nonlinear, curved relationship, which isn’t what simple linear regression models. And a form like y = a x + b would still describe a straight line, but it labels the slope and intercept differently from the standard convention used in this context, making it less consistent with the typical parameter naming.

A straight-line relationship expresses y as a constant plus a term proportional to x. In simple linear regression, the model is y = intercept + slope × x. This means y changes by the slope amount for each unit change in x, and when x is zero, y is at the intercept level.

The form y = b x + a matches that idea, with a as the intercept and b as the slope. It’s the same relationship as y = a + b x, just written with the terms swapped. This is why it’s the best representation here.

The squared term would imply a nonlinear, curved relationship, which isn’t what simple linear regression models. And a form like y = a x + b would still describe a straight line, but it labels the slope and intercept differently from the standard convention used in this context, making it less consistent with the typical parameter naming.