Null hypothesis for multiple linear regression

1. Null-hypothesis for a
Multiple-Linear Regression
Conceptual Explanation

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

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

4. 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.

5. 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).

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

7. Template #1

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

9. Here is an example:

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

11. 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].

12. 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].

13. 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].

14. 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].

15. 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].

16. 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].

17. 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

18. 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].

19. 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].

20. 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].

21. 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].

22. 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].

23. 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.

24. Template #2

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

26. 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].

27. 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].

28. 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].

29. 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].

30. 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].

31. 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.

32. 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.

33. 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.

34. 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.

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

36. 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.

37. 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.

38. 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.

39. 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.

40. 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.