Consider the following simple linear regression model: y = β₀ + β₁x + ε. When determining whether there is a negative linear relationship between x and y, the alternative hypothesis takes the form ________. A) H_A: β₁ = 0 B) H_A: β₁ 0 C) H_A: β₁ 0

Question

Consider the following simple linear regression model: y = β₀ + β₁x + ε. When determining whether there is a negative linear relationship between x and y, the alternative hypothesis takes the form ________. A) H_A: β₁ = 0 B) H_A: β₁ > 0 C) H_A: β₁ < 0 D) H_A: b₁ > 0

Quizplus · Accepted Answer

The alternative hypothesis for determining a negative linear relationship between x and y is that the coefficient β₁ is negative (i.e., less than 0). Therefore, option C is the correct choice. Option A assumes that there is no linear relationship between x and y, while option B and D assume a positive linear relationship, which is not the hypothesis being tested.

Consider the Following Simple Linear Regression Model: Y = β0

Consider the Following Simple Linear Regression Model: Y = β₀