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If β1= β2=0 and β3= 0 is null hypothesis.

If β1= β2=0 holds and β3= 0 fails to hold, then what can you conclude?

Does it mean there is a strong correlation between x1 and x2? or There is a linear relationship between the outcome variable(Y) and x3?

Bhuneshwer
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  • I think you can better ask this question on stats.stackexchange.com as is it not really programming related. FYI, the null hypothesis in multiple regression is that your model with predictor variables included predicts better than the empty model (So without any predictors). – Psychotechnopath Feb 02 '19 at 06:46
  • No, it means there is a statistically significant difference between beta_3 and the reference level (I assume beta_1). – user2974951 Feb 04 '19 at 09:48

3 Answers3

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There is a linear relationship between the outcome variable(Y) and x3.

Since β3=0 fails to hold, it means that x3 is a significant variable in this linear regression model. Thus, we can say that there is a linear relationship between the outcome variable (Y) and x3.

Archana
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There is a linear relationship between the outcome variable(Y) and x3

user14350821
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There is no linear relationship between y and any of the three independent variables.

Naresh Kumar
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