Example of Simple Regression

A materials engineer at a furniture manufacturing site wants to assess the stiffness of the particle board that the manufacturer uses. The engineer measures the stiffness and the density of a sample of particle board pieces.

The engineer uses simple regression to determine whether the density of the particles is associated with the stiffness of the board.

  1. Open the sample data, ParticleBoard.MTW.
  2. Open the Simple Regression dialog box.
    • Mac: Statistics > Regression > Simple Regression
    • PC: STATISTICS > Regression > Simple Regression
  3. In Response (Y), enter Stiffness.
  4. In Predictor (X), enter Density.
  5. On the Options tab, select Display 95% confidence interval and Display 95% prediction interval.
  6. On the Graphs tab, select Residual plots.
  7. Click OK.

Interpret the results

The p-value 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. However, there appears to be an outlier in the top right corner of the fitted line plot. This point corresponds to observation 21, which is shown in the table of Fits and Diagnostics for Unusual Observations. Because the outlier could have a strong effect on the results, the engineer should investigate this point to determine its cause.

Analysis of Variance
Source
DF
Adj SS
Adj MS
F-Value
P-Value
Model Summary
S
R-sq
R-sq(adj)
Coefficients
Term
Coef
SE Coef
T-Value
P-Value
Regression Equation
Fits and Diagnostics for Unusual Observations
Obs
Stiffness
Fit
Resid
Std Resid
 
R Large residual
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