# Interaction in linear regression

#### Almostasmartstudent

##### New Member
Hello everyone,

currently I'm doing research about the relation between body weight and the social status of children, but I'm stuck. I hope somebody can help me with the interpretation of the interaction terms in SPSS. Below I explain my model and my hypothesis briefly:

I hypothesize that girls are more vulnerable for status loss than boys if they are overweight or obese.

The model that I build is as follows:
- Social status is my dependent variable. (range is 1.00 - 5.00 (1 means very low and 5 means very high)
- Age and ethnicity are my control variables. Age is a continuous variabel, ethnicity is a binary one (Swedish and not Swedish)
- Overweight (1 means overweight, 0 means not overweight) (I made a dummy for this one) (a normal weight is the reference group)
- Obese (1 means obese, 0 means not obese) (I made a dummy for this one) (a normal weight is the reference group)
- Gender (1 = male, 0 = female)
- 2 interaction terms (overweight * gender) and (obese * gender)

My model is as follows:
Y = 4.4004 + 0.041*ethnicity - 0.071*age - 0.390*overweight - 1.040*Obese - 0.353*gender - 0.168*overweight*gender + 0.856*obese*gender

My question is: how can I interpret both the interaction term in relation to my hypothesis?

#### Omerikooo

##### New Member
Hello,

I can help you about the interpretation but why do you include both obese and overweight at the same time. Couldn't you use only one variable including reference, overweight and obese. This would make better sense.

For a female obese:

Y = 4.4004 + 0.041*ethnicity - 0.071*age - 0.390*(1) - 1.040*(1) - 0.353*(0) - 0.168*(1)*(0) + 0.856*(1)*(0)

Y = 4.4004 + 0.041*ethnicity - 0.071*age - 0.390 - 1.040

Y = 4.4004 - 0.390 - 1.040 + 0.041*ethnicity - 0.071*age

Y = 2,9704 + 0.041*ethnicity - 0.071*age

your model would look like this.

But again, you should first fix the issue about the overweight and obese variables.

#### Almostasmartstudent

##### New Member
Hello,

I can help you about the interpretation but why do you include both obese and overweight at the same time. Couldn't you use only one variable including reference, overweight and obese. This would make better sense.

For a female obese:

Y = 4.4004 + 0.041*ethnicity - 0.071*age - 0.390*(1) - 1.040*(1) - 0.353*(0) - 0.168*(1)*(0) + 0.856*(1)*(0)

Y = 4.4004 + 0.041*ethnicity - 0.071*age - 0.390 - 1.040

Y = 4.4004 - 0.390 - 1.040 + 0.041*ethnicity - 0.071*age

Y = 2,9704 + 0.041*ethnicity - 0.071*age

your model would look like this.

But again, you should first fix the issue about the overweight and obese variables.
Thanks! I needed to split them for my other hypothesis, which didn't require an interaction. The teacher said that my model was good...

#### Omerikooo

##### New Member
Okay. If you are okay with it no problem.

#### hlsmith

##### Less is more. Stay pure. Stay poor.
What is your sample size and can you just use their weight or BMI as a continuous variable, so that you don't loss information?

#### Almostasmartstudent

##### New Member
What is your sample size and can you just use their weight or BMI as a continuous variable, so that you don't loss information?
Well that is the sad part of it; I can't use BMI as a continuous variable if I want to say something about obesity, because you can't compare the BMI of a 10 year old girl with a 13-years-old boy, so I had to create 3 categories. Based on a different BMI range for every age and sex group, they had to be categorized. That is why I can't use it as a continuous variabele. And the sample size 2230, but there are 69 missing values for BMI.

#### Karabiner

##### TS Contributor
My question is: how can I interpret both the interaction term in relation to my hypothesis?
You could create a graph with Y for normal weight males and females, overweight male and females, and obese males and females,
something similar to this and/or to this.

With kind regards

Karabiner

#### Omerikooo

##### New Member
Well that is the sad part of it; I can't use BMI as a continuous variable if I want to say something about obesity, because you can't compare the BMI of a 10 year old girl with a 13-years-old boy, so I had to create 3 categories. Based on a different BMI range for every age and sex group, they had to be categorized. That is why I can't use it as a continuous variabele. And the sample size 2230, but there are 69 missing values for BMI.

I don't understand why not ? You can use BMI as a continuous variable and introduce an interaction variable with age group. For example

Y = Intercept + Beta1*BMI +Beta2*BMI*(Age Category = Adolescents) + Beta3*BMI*(Age Category = Adult)

This model would adjust BMI coefficient according to age category.

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Correct, you would want to visualize that BMI does not have a nonlinear relationship with dependent variable, but you could absolutely use it as a continuous variable.

I use the following example all of the time: say you have two people, person A woke up late today, so skipped breakfast and drank a coffee (diuretic) and had a BMI of 29.9. The other person woke up on time, ate a breakfast, and had a BMI 30.0. This two people are exchangeable on pretty much every day, But you are saying they are categorically different and potentially masking the effect of BMI on you outcome. Loss of information. Also, using 3 categorical variables is eating up a truck load of degrees of freedom given you are looking at interaction terms.