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If I have data with a continuous outcome variable (yvar), age and gender and I run regression as follows (R code): 

summary(lm(yvar~age+gender+age*gender, data=mydata))

How will be the regression output in case of each of following 3 plots between age, gender and yvar:

enter image description here

This question is related to: How to determine signficant difference between 2 curves?

Thanks for your help.

Edit: Assume age is significantly related to yvar. Will gender and age:gender be significantly related in each of three plots? Since gender has not effect in plot A, I think both gender and age:gender will not have a significant P-value in plot A.

Based on comments by @schwebels: 

            plot A   plot B       plot C
age         sig      sig          sig
gender      NS       sig or NS    sig
age:gender  NS       sig          NS
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rnso
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There is no indication of variance but let's assume the variance is small relative to the effect size Plot A: The effect of age on yvar looks significantly greater than 0 for both F and M . (F and M start at the same yvar and increase at the same rate as a function of age). Plot B: The effect of age on yvar may be significantly greater than 0 for both F and M and the slope (the size of the effect) is possibly different between F and M. (F and M start at different yvar and increase at different rates as a function of age) Plot C: The effect of age on yvar may be significantly greater than 0 for both F and M, the slope is equivalent for F and M and the y-intercept may be significantly different between F and M. (F and M start at a different yvar and increase at the same rate as a function of age)

schwebels
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  • You have basically described the plots. The regression output gives coefficients and P value for age, gender and age:gender. What will be the P-values (significant or not) for these three parameter for three plots above? That is the main question. Lets assume age is significantly related to yvar. – rnso Dec 04 '14 at 15:41
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    Given that age is a significant predictor of yvar, plot A does not show a gender effect and therefore the gender*age interaction is not evaluated. In plot B gender modulates the effect of age on yvar and is significant. The age*gender interaction term is significant. In plot C gender is significant and gender*age is not significant because only the intercept is affected by gender, not the rate of change. – schwebels Dec 05 '14 at 15:39