If the pvalue is greater than the significance level, you cannot conclude that there is a statistically significant association between the response variable and the term. If you fit a quadratic model or a cubic model and the quadratic or cubic terms are not statistically significant, you may want to select a different model.
 

In these results, the pvalue for density is less than 0.0001, which is less than the significance level of 0.05. These results indicate that the association between stiffness and density is statistically significant.
If the pvalue of the term is significant, you can examine the regression equation and the coefficients to understand how the term is related to the response.
Use the regression equation to describe the relationship between the response and the terms in the model. The regression equation is an algebraic representation of the regression line. The regression equation for the linear model takes the following form: y = b_{0} + b_{1}x_{1}. In the regression equation, y is the response variable, b_{0} is the constant or intercept, b_{1} is the estimated coefficient for the linear term (also known as the slope of the line), and x_{1} is the value of the term.
The coefficient of the term represents the change in the mean response for a oneunit change in that term. The sign of the coefficient indicates the direction of the relationship between the term and the response. If the coefficient is negative, as the term increases, the mean value of the response decreases. If the coefficient is positive, as the term increases, the mean value of the response increases.
For example, a manager determines that an employee's score on a job skills test can be predicted using the regression model y = 130 + 4.3x. In the equation, x is the hours of inhouse training (from 0 to 20) and y is the test score. The coefficient, or slope, is 4.3, which indicates that, for every hour of training, the test score increases, on average, by 4.3 points.
For more information on coefficients, go to What is a regression coefficient?
 

In these results, the coefficient for the predictor, Density, is 3.5405. The average stiffness of the particle board increases by 3.5405 for every 1 unit increase in density. The sign of the coefficient is positive, which indicates that as density increases, stiffness also increases.
R^{2} is the percentage of variation in the response that is explained by the model. The higher the R^{2} value, the better the model fits your data. R^{2} is always between 0% and 100%.
R^{2} always increases when you add additional predictors to a model. For example, the best fivepredictor model will always have an R^{2} that is at least as high the best fourpredictor model. Therefore, R^{2} is most useful when you compare models of the same size.
Use adjusted R^{2} when you want to compare models that have different numbers of predictors. R^{2} always increases when you add a predictor to the model, even when there is no real improvement to the model. The adjusted R^{2} value incorporates the number of predictors in the model to help you choose the correct model.
Use predicted R^{2} to determine how well your model predicts the response for new observations. Models that have larger predicted R^{2} values have better predictive ability.
A predicted R^{2} that is substantially less than R^{2} may indicate that the model is overfit. An overfit model occurs when you add terms for effects that are not important in the population, although they may appear important in the sample data. The model becomes tailored to the sample data and therefore, may not be useful for making predictions about the population.
Predicted R^{2} can also be more useful than adjusted R^{2} for comparing models because it is calculated with observations that are not included in the model calculation.
Small samples do not provide a precise estimate of the strength of the relationship between the response and predictors. If you need R^{2} to be more precise, you should use a larger sample (typically, 40 or more).
R^{2} is just one measure of how well the model fits the data. Even when a model has a high R^{2}, you should check the residual plots to verify that the model meets the model assumptions.
 

In these results, the density of the particle board explains 84.47% of the variation in the stiffness of the boards. The R^{2} value indicates that the model fits the data well. The adjusted R^{2} is 83.89%, and the predicted R^{2} is 80.83%. The R^{2} and predicted R^{2} values are relatively close, which indicates that the model can be used for predicting future response values.
Use the residual plots to help you determine whether the model is adequate and meets the assumptions of the analysis. If the assumptions are not met, the model may not fit the data well and you should use caution when you interpret the results.
Use the residuals versus fits plot to verify the assumption that the residuals are randomly distributed and have constant variance. Ideally, the points should fall randomly on both sides of 0, with no recognizable patterns in the points.
Pattern  What the pattern may indicate 

Fanning or uneven spreading of residuals across fitted values  Nonconstant variance 
Curvilinear  A missing higherorder term 
A point that is far away from zero  An outlier 
A point that is far away from the other points in the xdirection  An influential point 
Use the normal probability plot of residuals to verify the assumption that the residuals are normally distributed. The normal probability plot of the residuals should approximately follow a straight line.
Pattern  What the pattern may indicate 

Not a straight line  Nonnormality 
A point that is far away from the line  An outlier 
Changing slope  An unidentified variable 
For more information on how to handle patterns in the residual plots, go to Interpret all statistics and graphs for Simple Regression and click the name of the residual plot in the list at the top of the page.