Line plots typically contain the following elements:

·    A y-axis representing the variable function

·    An x-axis representing levels of a factor

·    A legend containing the levels of a second factor

·    Lines connecting the values of factor-level pairs while holding the legend factor constant

Line plots are particularly helpful for identifying relationships between two factors and the response. To identify possible relationships, look for the following:

·    Sloped lines suggesting an effect due to the x-axis factor

·    Differences between lines suggesting a difference due to the legend factor

·    Non-parallel lines suggesting an interaction effect

For the textile strength data, the non-zero slope of all lines suggests differences in the mean strength between operators. Operator 1 generally produced the lowest mean strength regardless of the machine used, while operator 3 produced the highest mean strength.

On the other hand, the effect of machine is not consistent. Any given machine produces a high or low mean strength depending on the operator. The non-parallel line associated with operator 1 on machine 2 suggests a possible interaction. This combination produced an unexpectedly high mean strength that may warrant a follow-up investigation.

Overall, operator appears to be a strong factor in textile strength. The machine's effect on strength is less pronounced and possibly statistically insignificant. Additionally, there may be an interaction effect. To determine if these effects are statistically significant, conduct an appropriate test such as an ANOVA.