Consider the following simple linear regression model: y = β₀ + β₁x + ε. When determining whether x significantly influences y, the null hypothesis takes the form ________. A) H₀: β₁ = 0 B) H₀: β₁ = 1 C) H₀: b₁ = 0 D) H₀: b₁ = 1

Question

Quizplus · Accepted Answer

The null hypothesis in a simple linear regression model when testing whether x significantly influences y is typically that the coefficient on x (β) is equal to 0 (i.e. there is no significant relationship between x and y). Therefore, choice A is the correct answer as it specifies the null hypothesis in this form. Choices B and D are incorrect as they state that the coefficient on x is equal to 1, which is not the null hypothesis. Choice C is also incorrect as it uses the estimate of the coefficient (b) rather than the true parameter (β) in the null hypothesis.

Consider the Following Simple Linear Regression Model: Y = β0

Consider the Following Simple Linear Regression Model: Y = β₀