Question

What is the purpose of testing whether β1 = 0? The purpose of testing whether β1 = 0 is to determine whether or not the mean of the x values is equal to the mean of the y values. The purpose of testing whether β1 = 0 is to determine whether or not the regression line provides a good fit for the data. The purpose of testing whether β1 = 0 is to determine whether or not there is a significant relationship between x and y. The purpose of testing whether β1 = 0 is to determine whether or not there is a cause-and-effect relationship between x and y.

Answer 1

Answer:

The purpose of testing whether β1 = 0 is to determine whether or not there is a significant relationship between x and y

Step-by-step explanation:

• The purpose of testing whether β1 = 0 is to determine whether or not the mean of the x values is equal to the mean of the y values.

No, since we are not interested if the mean for the two variables x and y are equal, we want to know if we have relationship between the two variables.

• The purpose of testing whether β1 = 0 is to determine whether or not the regression line provides a good fit for the data

No, if we want to test if the regression line provides a good fit for the data we need to use a Chi square test or other type of test.

• The purpose of testing whether β1 = 0 is to determine whether or not there is a significant relationship between x and y

Yes, the idea when we have this system of hypothesis:

Null hypothesis: $\beta_1 =0$

Alternative hypothesis: $\beta_1 \neq 0$

Is see if we have a significant relationship between x and y, that means that the slope is not equal to 0.

• The purpose of testing whether β1 = 0 is to determine whether or not there is a cause-and-effect relationship between x and y.

No, when we conduct a regression we never can conclude that we have a cause-relation effect, that's not the goal when we conduct this, the idea is check if we have a type of relationship that can be linear, quadratic or other type of relationship betwen some variables.