In a simple linear regression analyzing the relationship between candy amount and blood sugar levels, what does Ho: B1 = 0 represent?

In a simple linear regression analyzing the relationship between candy amount and blood sugar levels, what does Ho: B1 = 0 represent?

• A. There is no linear relationship between candy amount and blood sugar levels.
• B. There is a positive linear relationship between candy amount and blood sugar levels.
• C. The slope is equal to 1.
• D. The intercept is zero.

Answer: (A)

In simple linear regression, Ho: B1 = 0 tests whether the slope is zero. The slope B1 shows how much the response changes on average for a one-unit change in candy amount. If the slope is zero, changing the candy amount has no linear effect on blood sugar, so the regression line would be flat and there’s no linear relationship. It’s possible there could be some non-linear pattern, but within this linear model there’s no linear association. This statement does not involve the intercept or any specific slope value like 1, and it doesn’t imply a positive or negative relationship—those would correspond to a nonzero B1.

In simple linear regression, Ho: B1 = 0 tests whether the slope is zero. The slope B1 shows how much the response changes on average for a one-unit change in candy amount. If the slope is zero, changing the candy amount has no linear effect on blood sugar, so the regression line would be flat and there’s no linear relationship. It’s possible there could be some non-linear pattern, but within this linear model there’s no linear association. This statement does not involve the intercept or any specific slope value like 1, and it doesn’t imply a positive or negative relationship—those would correspond to a nonzero B1.