How can know the interaction between two predictors variable, and how can interpret?

Question

How can analyze if two variables exist an interaction?

I am doing a linear regression with two variables, and with two variables and interaction variables, and I am getting the following results:

lm(formula = rta ~ exp1 * exp3, data = datos)
Residuals:
    Min      1Q  Median      3Q     Max 
-3.3226 -0.4722  0.0434  0.5502  2.3274 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)  
(Intercept)  48.4389    22.2931   2.173   0.0408 *
exp1          0.3055     0.2580   1.184   0.2490  
exp3        -16.3179    12.2794  -1.329   0.1975  
exp1:exp3     0.1446     0.1424   1.015   0.3210  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.147 on 22 degrees of freedom
Multiple R-squared:  0.8939,    Adjusted R-squared:  0.8795 
F-statistic:  61.8 on 3 and 22 DF,  p-value: 7.031e-11

> modelo <- lm(data = datos,formula = rta ~ exp1+exp3)
> summary(modelo)

Call:
lm(formula = rta ~ exp1 + exp3, data = datos)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.7130 -0.3310  0.0774  0.6270  1.8270 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 26.47311    5.37307   4.927 5.59e-05 ***
exp1         0.56000    0.06078   9.214 3.50e-09 ***
exp3        -3.86042    0.45663  -8.454 1.64e-08 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 1.147 on 23 degrees of freedom
Multiple R-squared:  0.889, Adjusted R-squared:  0.8793 
F-statistic: 92.06 on 2 and 23 DF,  p-value: 1.055e-11

The main question, here is how can interpret those results, and how can know if exists any interaction between those two predictors variables exp1 and exp2

Thanks

Answer 1

Generally, a linear interaction between two predictors on an outcome means that the relationship between each predictor on the outcome depends (linearly) on the level of the other predictor. In your example, that would mean that the slope of exp1 on rta depends on the level of exp3.

The interpretation of the "main effects" in a regression with interactions is the slope of that variable on the outcome when the other covariate is held at zero. So, in your example, when exp3 is equal to zero, the slope of exp1 on rta is 0.3055, and when exp1 is equal to zero, the slope of exp3 on rta is -16.3179. It may be that exp1 and exp3 cannot even take on the value of zero or they don't in your dataset, in which case these slopes are meaningless or extrapolations.

The interpretation of the interaction coefficient is the change in the slope of one predictor corresponding to a one-unit change in the other predictor. So, for every one-unit increase in exp3, the slope of exp1 on rta is expected to increase by 0.1446, and for every one-unit increase in exp1, the slope of exp3 on rta is expected to increase by 0.1446.

The p-value on the interaction coefficient tells you whether you have evidence to claim an interaction is present. Because you have a high p-value on the interaction, there is not enough evidence to claim that an interaction is present. You do have evidence to claim that the effects of exp1 and exp3 on rta are present, but there isn't evidence to claim that the effects of each predictor depend on the other.