Null hypothesis for multiple linear regression

Null-hypothesis for a Multiple-Linear Regression

Conceptual Explanation

With hypothesis testing we are setting up a null-hypothesis –

With hypothesis testing we are setting up a null-hypothesis – the probability that there is no effect or relationship –

With hypothesis testing we are setting up a null-hypothesis – the probability that there is no effect or relationship – and then we collect evidence that leads us to either accept or reject that null hypothesis.

As you may recall, when running a Multiple-Linear Regression you are attempting to determine the predictive power of more than one independent (hours of sleep, study time, gender, family background, etc.) on a dependent variable (test scores).

Here are two templates for a Multiple Linear Regression Null-Hypotheses:

Template #1

There will be no significant prediction of [insert dependent variable] by [insert predictor variable 1] and [insert predictor variable 2], etc.

Here is an example:

You have been asked to investigate how well hours of sleep, study time, gender, mother’s education predicts ACT scores.

Null-hypothesis #1 for:

You have been asked to investigate how well hours of sleep, study time, gender, mother’s education predicts ACT scores.

There will be no significant prediction of [insert dependent variable] by [insert predictor variable 1], [insert predictor variable 2], [insert predictor variable 3], & [insert predictor variable 4].

Null-hypothesis #1 for:

You have been asked to investigate how well hours of sleep, study time, gender, mother’s education predicts ACT scores.

There will be no significant prediction of [insert dependent variable] by [insert predictor variable 1], [insert predictor variable 2], [insert predictor variable 3], & [insert predictor variable 4].

Null-hypothesis #1 for:

You have been asked to investigate how well hours of sleep, study time, gender, mother’s education predicts ACT scores.

There will be no significant prediction of [insert dependent variable] by [insert predictor variable 1], [insert predictor variable 2], [insert predictor variable 3], & [insert predictor variable 4].

Null-hypothesis #1 for:

You have been asked to investigate how well hours of sleep, study time, gender, mother’s education predicts ACT scores.

There will be no significant prediction of [insert dependent variable] by [insert predictor variable 1], [insert predictor variable 2], [insert predictor variable 3], & [insert predictor variable 4].

Null-hypothesis #1 for:

You have been asked to investigate how well hours of sleep, study time, gender, mother’s education predicts ACT scores.

There will be no significant prediction of ACT scores by [insert predictor variable 1], [insert predictor variable 2], [insert predictor variable 3], & [insert predictor variable 4].

Null-hypothesis #1 for:

You have been asked to investigate how well hours of sleep, study time, gender, mother’s education predicts ACT scores.

There will be no significant prediction of ACT scores by [insert predictor variable 1], [insert predictor variable 2], [insert predictor variable 3], & [insert predictor variable 4].

Null-hypothesis #1 for:

You have been asked to investigate how well hours of sleep, study time, gender, mother’s education predicts ACT scores.

There will be no significant prediction of ACT scores by hours of sleep, [insert predictor variable 2], [insert predictor variable 3], & [insert predictor variable 4]. f

Null-hypothesis #1 for:

You have been asked to investigate how well hours of sleep, study time, gender, mother’s education predicts ACT scores.

There will be no significant prediction of ACT scores by hours of sleep, [insert predictor variable 2], [insert predictor variable 3], & [insert predictor variable 4].

Null-hypothesis #1 for:

You have been asked to investigate how well hours of sleep, study time, gender, mother’s education predicts ACT scores.

There will be no significant prediction of ACT scores by hours of sleep, study time, [insert predictor variable 3], & [insert predictor variable 4].

Null-hypothesis #1 for:

You have been asked to investigate how well hours of sleep, study time, gender, mother’s education predicts ACT scores.

There will be no significant prediction of ACT scores by hours of sleep, study time, [insert predictor variable 3], & [insert predictor variable 4].

Null-hypothesis #1 for:

You have been asked to investigate how well hours of sleep, study time, gender, mother’s education predicts ACT scores.

There will be no significant prediction of ACT scores by hours of sleep, study time, gender & [insert predictor variable 4].

Null-hypothesis #1 for:

You have been asked to investigate how well hours of sleep, study time, gender, mother’s education predicts ACT scores.

There will be no significant prediction of ACT scores by hours of sleep, study time, gender & [insert predictor variable 4].

Null-hypothesis #1 for:

You have been asked to investigate how well hours of sleep, study time, gender, mother’s education predicts ACT scores.

There will be no significant prediction of ACT scores by hours of sleep, study time, gender & mother’s education.

Template #2

In the presence of the others , there will be no significant prediction of [insert the dependent variable] by [insert the first independent variable].

Null-hypothesis #2a for:

You have been asked to investigate how well hours of sleep, study time, gender, mother’s education predicts ACT scores.

In the presence of the others , there will be no significant prediction of [insert the dependent variable] by [insert the first independent variable].

Null-hypothesis #2a for:

You have been asked to investigate how well hours of sleep, study time, gender, mother’s education predicts ACT scores.

In the presence of the others , there will be no significant prediction of [insert the dependent variable] by [insert the first independent variable].

Null-hypothesis #2a for:

You have been asked to investigate how well hours of sleep, study time, gender, mother’s education predicts ACT scores.

In the presence of the others , there will be no significant prediction of [insert the dependent variable] by [insert the first independent variable].

Null-hypothesis #2a for:

You have been asked to investigate how well hours of sleep, study time, gender, mother’s education predicts ACT scores.

In the presence of the others , there will be no significant prediction of [insert the dependent variable] by [insert the first independent variable].

Null-hypothesis #2a for:

You have been asked to investigate how well hours of sleep, study time, gender, mother’s education predicts ACT scores.

In the presence of the others , there will be no significant prediction of ACT scores by [insert the first independent variable].

Null-hypothesis #2a for:

You have been asked to investigate how well hours of sleep, study time, gender, mother’s education predicts ACT scores.

In the presence of the others , there will be no significant prediction of ACT scores by hours of sleep.

Null-hypothesis #2b for:

You have been asked to investigate how well hours of sleep, study time, gender, mother’s education predicts ACT scores.

In the presence of the others , there will be no significant prediction of ACT scores by study time.

Null-hypothesis #2c for:

You have been asked to investigate how well hours of sleep, study time, gender, mother’s education predicts ACT scores.

In the presence of the others , there will be no significant prediction of ACT scores by gender.

Null-hypothesis #2d for:

You have been asked to investigate how well hours of sleep, study time, gender, mother’s education predicts ACT scores.

In the presence of the others , there will be no significant prediction of ACT scores by mother’s education.

In summary – here are the null hypotheses for this example:

Ho 1: There will be no significant prediction of ACT scores by hours of sleep, study time, gender & mother’s education.Ho 2a: In the presence of the others , there will be no significant prediction of ACT scores by hours of sleep.Ho 2b: In the presence of the others , there will be no significant prediction of ACT scores by study time.Ho 2c: In the presence of the others , there will be no significant prediction of ACT scores by mother’s education.Ho 2d: In the presence of the others , there will be no significant prediction of ACT scores by gender.

Ho 1: There will be no significant prediction of ACT scores by hours of sleep, study time, gender & mother’s education.Ho 2a: In the presence of the others , there will be no significant prediction of ACT scores by hours of sleep.Ho 2b: In the presence of the others , there will be no significant prediction of ACT scores by study time.Ho 2c: In the presence of the others , there will be no significant prediction of ACT scores by mother’s education.Ho 2d: In the presence of the others , there will be no significant prediction of ACT scores by gender.

Ho 1: There will be no significant prediction of ACT scores by hours of sleep, study time, gender & mother’s education.Ho 2a: In the presence of the others , there will be no significant prediction of ACT scores by hours of sleep.Ho 2b: In the presence of the others , there will be no significant prediction of ACT scores by study time.Ho 2c: In the presence of the others , there will be no significant prediction of ACT scores by mother’s education.Ho 2d: In the presence of the others , there will be no significant prediction of ACT scores by gender.

Ho 1: There will be no significant prediction of ACT scores by hours of sleep, study time, gender & mother’s education.Ho 2a: In the presence of the others , there will be no significant prediction of ACT scores by hours of sleep.Ho 2b: In the presence of the others , there will be no significant prediction of ACT scores by study time.Ho 2c: In the presence of the others , there will be no significant prediction of ACT scores by gender.Ho 2d: In the presence of the others , there will be no significant prediction of ACT scores by mother’s education.y gender.

Ho 1: There will be no significant prediction of ACT scores by hours of sleep, study time, gender & mother’s education.Ho 2a: In the presence of the others , there will be no significant prediction of ACT scores by hours of sleep.Ho 2b: In the presence of the others , there will be no significant prediction of ACT scores by study time.Ho 2c: In the presence of the others , there will be no significant prediction of ACT scores by gender.Ho 2d: In the presence of the others , there will be no significant prediction of ACT scores by mother’s education.