# Scale interaction effect

grades-occupation – 1scale

Hypothesis: With the improvement in student’s grades the gap/the difference between the intention of those students whose father works as a white collar and the intention of those students whose father works as a blue collar drops/decreases.

**Dependent variable**: Intention to apply to higher education

**Independent variables**: mean of grades – scale, father’s occupation (0-blue collar, 1-white collar) – dummy, inter (grades*fatheroccup)

The database contains the answers of 120 students. The mean grades refer to the general school grades. The intention to apply to higher education was measured on a 7 point scale, where 1 means absolutely not and 7 means absolutely yes. The other independent variable is a dummy variable (father’s occupation), so there is no need to recode it.

Ŷ=b0+b1*MeanOfGrades+b2*FathersOccup+b3*inter

Ŷ=b0+b1*MeanOfGrades+b2*FathersOccup+b3*(MeanOfGrades*FathersOccup)

Ŷ=b0+b2*FathersOccup+(b1+b3*FathersOccup)*MeanOfGrades

**b2 (dummy): The difference in the average level of the dependent variable between the categories of this independent variable, when the other independent variable is 0 (the mean of grade is 0).**

b2: The difference in the average level of intention between those students’s whose father has a white collar job and those students whose father has a blue collar job when the mean of grades is 0. Since basically none of our respondents achieved a 0 grade, in this case the value of b2 is not meaningful.

**b3(inter): if the scale independent variable increases by 1 unit, then how much will be the effect of the dummy variable. If the scale independent variable will increase by 1 unit then the difference between the two groups (the categories of this dummy variable) will increase/decrease this much.**

b3(inter): If the mean of the grades increases by one unit, then the effect of the father’s occupation will decrease by 0.97.

**b1:** We usually select some of the characteristics of this variable and we interpret this coefficient in terms of these characteristics, for instance: the average, the average – 1 standard deviation, the average + 1 standard deviation. In our example the average of the grades is 4,05, it’s standard deviation is 0,82. So, these three values are the followings: 4,05, 3,23, 4,87.

The average is 4,05. The Std. Deviation is 0,82. This you can see if before running the regression in the “Statistics” option you mark the Descriptives.

Mean of the grades | The effect of the father’s occupation |

average – 1 Std. deviation (3,23) | (b2+b3*MeanOfGrades)= 5,12-(0,97*3,23)=1,98 |

average (4,05) | (b2+b3*MeanOfGrades)= 5,12-(0,97*4,05)=1,18 |

average + 1 Std. deviation (4,87) | (b2+b3*MeanOfGrades)= 5,12-(0,97*4,87)=0,38 |

We can clearly see from the above table how the effect of the father’s occupation decreases. (We compare the numbers: 1,98, 1,18, 0,38).

Among those whose grades are below the average the difference is only 1,98, among those who have an average grade the difference is 1,18 and among those whose grades are above the average it is 0,38.

In conclusion, the results show that students from the poorer families intend to apply to higher education because of the cost and benefit related reasons, since the father’s occupation clearly has an effect on the intention of the respondents to apply to higher education.

Now let’s calculate the average estimated intention of those students whose father works as a blue collar and for those whose father works as a white collar.

Students whose grades are 1 Standard deviation below the average and their father is a blue collar the FathersOccup is 0 and the MeanOfGrades is 3,23. In their case we can write down the following equation:

Ŷ=b0+b1*MeanOfGrades+b2*FathersOccup+b3*(MeanOfGrades*FathersOccup)

Ŷ=b0+b1*3,23+b2*0+b3*0*3,23= -1,76+1,57*3,23=3,31.

We also want to find out the estimated average intention of the students among those whose father is a blue collar and among those whose father is a white collar.

Students whose grades are 1 Standard deviation below the average and their father is a white collar the FathersOccup is 1 and the MeanOfGrades is 3,23. In their case we can write down the following equation:

Ŷ=b0+b1*3,23+b2*1+b3*1*3,23= -1,76+5,03-3,14=5,25

Mean of the Grade | Blue Collar | White collar |

average – 1 Std. Deviation (3,23) | 3,31 | 5,25 |

average (4,05) | 4,60 | 5,80 |

average + 1 Std. Deviation (4,87) | 5,88 | 6,22 |

The result shows that the decreasing difference between the intentions to apply to higher education of students whose father is a blue collar and of those whose father is a white collar can be more strongly explained by the decision/behaviour of those students whose father is a blue collar. So, the intentions of the students who have a blue collar father depends more strongly on their previous grades than the intentions of those students whose father is a white collar. We can state this because as the mean grade increases from 3,23 to 4,87 the average intention to apply to higher education among students whose father works as blue collar increases from 3,31 to 5,88, so it increases by 2,57; while among those students whose father works as a white collar it increases only by 0,97 (6,22-5,25). This means that the regression line is much steeper in the case of blue collars than in the case of white collars.

**Check the following more general explanation of b2 (dummy) and b3 (inter) coefficients:**

## Another example: trust, tvhours – 1 scale

Dependent: SEI10 – Respondent’s socioeconomic index

Independent: TRUST – Can people be trusted, TVHOURS – Hours per day watching TV

Recode the TRUST variable, since it is not a dummy variable. 1 – trust, 0-no trust (can’t be too careful, depends). Create the inter variable and run the regression.

**b1 (dummy): The difference in the average level of the dependent variable between the categories of this independent variable, when the other independent variable is 0 (the mean of grade is 0).**

b1: In a hypothetical case, when someone does not watch TV at all then the average socioeconomic index for those who believe that people can be trusted is 17.226 higher than for those who believe that people cannot be trusted. (p<0,001)

**b3 (inter): if the scale independent variable increases by 1 unit, then how much will be the effect of the dummy variable. If the scale independent variable will increase by 1 unit then the difference between the two groups (the categories of this dummy variable) will increase/decrease this much.**

b3 (inter): If someone watches TV one hour more in a day then the effect of trust will be -3,680. So, if someone watches TV one hour more in a day the socioeconomic status of those who believe that people can be trusted will be 3.680 less then those who believe that people cannot be trusted. (p<0,05)