What can I do when the p-value of my regression is not significant? I tried to transform it with log or sqrt, it improved a little, but not enough to go below the 5%.

The residuals follow a Normal distribution and there is no strong correlation between the variables.

Does it mean the linear regression just doesn't fit my data or, because the p-value is close to the threshold, I can ignore it?

Edit :

I did a cumulative coding because there were lots of categorical and ordinal variable, that explain the difference between the R^2 and ajusted R^2, see below the functionnement (not my data, just for the explanation)

## Best Answer

One interpretation of a high p-value in a regression model is that your model doesn't produce better predictions than a model that left out everything except the intercept.

This can happen if some of the predictors you used are unrelated or only weakly related to the response. Estimating coefficients for those predictors makes your other estimates worse. In your case, you are including 15 predictors in a dataset of 24 observations, so it shouldn't be surprising that you can't get good estimates of all 15 coefficients.

The usual solution to this is to simplify your model. Running all possible subsets of your predictors can find the model with the best p-value, but will also make your p-value artificially small. (The selected F statistic won't have an F distribution under the null hypothesis.) There are several strategies for dealing with this, all with pitfalls, so automatic selection is likely to be unreliable; you should consult a good regression text or a local expert.