In simple linear regression, most often we perform a two-tail test of the population slope $\beta _ { 1 }$ to determine whether there is sufficient evidence to infer that a linear relationship exists. Which of the following best describes the null and alternative hypotheses needed for a test of significance?
A)Ho:$\beta$0 = 0 HA:$\beta$0 $\neq$ 0
B)Ho: $\beta$1 $\neq$ 0 HA: $\beta$1 = 0
C)Ho: $\beta$0 = 0 HA: $\beta$0 $\neq$ 1
D)Ho: $\beta$1 = 0 HA: $\beta$1$\neq$ 0

Question

In simple linear regression, most often we perform a two-tail test of the population slope $\beta _ { 1 }$ to determine whether there is sufficient evidence to infer that a linear relationship exists. Which of the following best describes the null and alternative hypotheses needed for a test of significance?
A)Ho:$\beta$0 = 0 HA:$\beta$0 $\neq$ 0
B)Ho: $\beta$1 $\neq$  0 HA: $\beta$1 = 0
C)Ho: $\beta$0 = 0 HA: $\beta$0 $\neq$ 1
D)Ho: $\beta$1 = 0 HA: $\beta$1$\neq$ 0

Quizplus · Accepted Answer

The correct null hypothesis (Ho) for testing the significance of the slope in simple linear regression is that the slope ($\beta_1$) is equal to 0, indicating no linear relationship. The alternative hypothesis (HA) is that the slope is not equal to 0, indicating a linear relationship exists.

In Simple Linear Regression, Most Often We Perform a Two-Tail β1\beta _ { 1 }β1​

In Simple Linear Regression, Most Often We Perform a Two-Tail $\beta _ { 1 }$