I would like to test how how gender interacts with another (continuous) variable. To do this, I am using a hierarchical (nested) regression model.

The first model uses the continuous variable and gender as predictors, but only the continuous variable is statistically significant.

In the second model, the continuous variable, gender, and the multiplicative interaction term are included as predictors, and all of them have a statistically significant effect.

Are the statistically significant relationships in the 2nd [fixed typo] model validly so? Why is gender non-significant in the first model, but significant in the second?

The first model uses the continuous variable and gender as predictors, but only the continuous variable is statistically significant.

In the second model, the continuous variable, gender, and the multiplicative interaction term are included as predictors, and all of them have a statistically significant effect.

Are the statistically significant relationships in the 2nd [fixed typo] model validly so? Why is gender non-significant in the first model, but significant in the second?

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