I have run my data on multiple regression with y= reading readiness as my dependent and 11 independent variables. The results of the minitab is attached. The result showed that regression model has R-sq of 29.9, Statistic= 6.40. But all the p-values of the potential predictors were greater than 0.05 (not significant).
Does it mean my regression equation is significant inspite of having insignificant predictors? I may have the wrong analysis on the regression results. How do we interpret the results of the multiple regression?
Your comments will help a lot. Thanks in advance
Yumi -
Both R-square and p-values are rather nebulous to interpret, especially p-values. Also, using 0.05 as a universal threshold is a practice you want to avoid. Effect size is not considered when you do that.
Further, the way 'independent' variables work together to 'predict' is important.
I suggest graphical residual analysis (predicted y values on the x-axis and estimated residuals on the y-axis) to study fit, and cross-validation to check for overfitting.
Best wishes - Jim
Dear Yumi,
Overfitting may be an issue, i.e. models with too many terms for the number of observations may produce misleading R-squared, regression coefficients, and p-values. Cross-validation is an option to detect overfitting if your sample size is reasonably big to allow partioning.
If the model specification is adequate, the results may just indicate that your sample size is too small to obtain significant p-values for the predictors.
Bests - Thomas
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