In linear regression, the interaction terms add significantly to the understanding of the relationship between the variables of the model allows multiple hypotheses to be tested. The disadvantage is that it is more difficult to interpret the regression parameters. This article describes how to interpret the estimates of regression parameters when there is a pattern of interaction.
The example is a model of the height of a shrub (height) by the amount of bacteria in the soil(Bacteria) and that the shrub is in part or in full sun (sun). The height is measured in cm, is measured in thousands of bacteria per ml of the Earth and Sun = 0, if the plant part, Sun and Sun = 1 if the plant in full sun. The regression equation was estimated as follows:
Height = 42 + 11 + 2.3 * Bacteria * Sun
It would be useful to add an interaction term of the model, if we wanted to test the hypothesis that the relationship between the amount of bacteria in the soil on whichHeight of the spot was different from that in full sun to part so One possibility is that in full sun, plants with more bacteria in the soil are greater, while in partial sun, plants are shorter with more bacteria in the soil, tend. Another possibility is that plants are more bacteria in the soil is greater than in either total or partial tend Sun, but that the relationship is much more dramatic in the middle part so
The presence of a significant interaction shows that theEffect of a predictor of target size is different at different values of the other predictor variable. It will be multiplied by adding a term of the model in which the two predictor variables tested. The regression equation will look like this:
Height = B0 + B1 + B2 + B3 * Bacteria * Sun * Sun * bacteria
Adding an interaction term, a model radically changed the interpretation of all coefficients. If there were no interaction term could be interpreted as B1,the only effect of bacteria on the size. Since the interaction indicates that the effect of bacteria on the top to different values of the Sun, the only effect of bacteria on height is not limited to B1, but it also depends on the values of so B1 and B3 + B3 * Sun: L ' unique effect of all bacteria is represented by bacteria that multiply in the model. B1 can now only as the effect of bacteria on height only if Sun can be interpreted = 0.
In our example, if you addConcept of interaction provides for our model as follows:
Height = 35 + 9 + 4.2 * 3.2 * + * Sun Bacteria Bacteria Sun
Note that adding the interaction term changes the values of B1 and B2. The effect of the bacteria level is now 4.2 + 3.2 * in the case of plants in partial sun, Sun = 0, so that the effect of bacteria is 4.2 + 3.2 * 0 = 4.2. So for two plants in partial sun, a plant with more than 1000 bacteria / ml in the world would probably be 4.2 cm greater than a plant with less bacteria. For plantsfull sun, but the effect of bacteria 4.2 + 3.2 * 1 = 7.4. So for two plants in full sun, a plant with more than 1000 bacteria / ml in the world would probably be 7.4 cm greater than a plant with less bacteria.
Because of the interactions, the effect is more bacteria in the soil in a different way, when a plant has been said, in whole or in part, so different that the slope of the regression between height and number of bacteria are different for different categories ofSun B3 shows how different the tracks.
B2 interpretation is more difficult. B2 is the effect of the sun, when the bacteria = 0. Since the bacteria is a continuous variable, it is unlikely that 0 is the same, if nothing else, B2, virtually meaningless in itself. Instead, it is useful to understand the effects of the sun, but again, this can be difficult. The effect of the sun is B2 + B3 * Bacteria, which is different for each of the infinite values of bacteria. For this reason, oftenThe only way is to get an intuitive understanding of the effects of the sun, some levels of bacteria in the plug equation, such as altitude, the target size to see the changes.
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