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I fitted a quadratic model on my data and got the following output:

model output

The Pr (>|t|) values were not significant (p<0.05) but the overall p-value of the model was. Is my model significant or not?

Zita Zimmermann
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    Welcome to Cross Validated! Does this answer your question? Why is it possible to get significant F statistic (p<.001) but non-significant regressor t-tests? – Dave Aug 08 '22 at 17:26
  • Thank you! There are a lot of useful informations in these posts explaining the reasons why this situation can occur. However, my original question was simply how to report this result (the significance of the model) in a publication? Which p value should I use? – Zita Zimmermann Aug 08 '22 at 17:47
  • What are your null and alternative hypotheses? – Dave Aug 08 '22 at 17:57
  • I fitted six different models to my data (linear, quadratic, exponential, 3rd, 4th and 5th degree polynomials) and I wanted to conclude which fits the best by comparing the R2 values of the six models. The output I showed above was from one of these curve fittings. I want to report the results of the analysis like "The quadratic model fits the data best (adjusted R2=0.7528, p=?)". So maybe I'm doing something wrong, but I did not formulate a null hypothesis before this analysis (or maybe the null hípothesis is that the quadratic model fits the data and the alternative is that it does not fit?) – Zita Zimmermann Aug 08 '22 at 18:15
  • You should know your null and alternative hypotheses before you run a hypothesis test. // 2) This kind of regression strategy is evocative of stepwise regression, which is known for its myriad issues. “Stepwise regression model-building is…pants. -Dr. Alexis Dinno
    • – Dave Aug 08 '22 at 18:25
  • Thank you, I will consider this! – Zita Zimmermann Aug 08 '22 at 19:05
  • @ZitaZimmermann , the way you've written your goal, I fitted six different models to my data, and I wanted to conclude which fits the best by comparing the R2 values of the six models. (adjusted R2=0.7528, p=?) , it sounds like you would focus on the overall p-value for the model, and not worry about the significance of the individual terms. ... Can I ask, are you fitting the exponential model also by OLS linear regression ( lm() ) ? – Sal Mangiafico Aug 08 '22 at 19:06
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    @Sal Mangiafico: Yes, I fitted the exponential model also with lm(). – Zita Zimmermann Aug 08 '22 at 19:11