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.

On the Options tab, select Display 95% confidence interval and Display 95% prediction interval.

On the Graphs tab, select Residual plots.

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

Regression

1

11552.8

11552.8

146.86

<0.0001

Error

27

2124.0

78.7

Total

28

13676.7

Model Summary

S

R-sq

R-sq(adj)

8.86937

84.47%

83.89%

Coefficients

Term

Coef

SE Coef

T-Value

P-Value

Constant

-21.534

4.735

-4.55

0.0001

Density

3.5405

0.2922

12.12

<0.0001

Regression Equation

Stiffness = −21.534 + 3.5405 Density

Fits and Diagnostics for Unusual Observations

Obs

Stiffness

Fit

Resid

Std Resid

21

96.305

69.1040

27.2010

3.33

R

R Large residual

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