Theoretical examples

Example 1 Suppose we want to examine the association between gender (x) and income (y). Gender has the values 0=Man and 1=Woman. Income is measured in thousands of Swedish crowns per month and ranges between 20 and 40. Let us assume that we get a B coefficient that is -1.3. That means that women have (on average) 1300 SEK less in monthly income compared to men.

Example 2 Suppose we want to examine the association between having young children (x) and the number of furry pets (y). Having young children is measured as either 0=No young children and 1=Young children. The number of furry pets is measured as the number of cats, dogs, or other furry animals living in the household, and ranges between 0 and 10. We get a B coefficient that is 0.98. In other words, those who have young children have (on average) almost one additional furry pet compared to those without young children.

Practical example

Dataset

StataData1.dta

Variable name	gpa
Variable label	Grade point average (Age 15, Year 1985)
Value labels	N/A

Variable name	bullied
Variable label	Exposure to bullying (Age 15, Year 1985)
Value labels	0=No 1=Yes

sum gpa bullied if pop_linear==1

The variable bullied is a binary variable with two categories: 0=No, 1=Yes. When we add it to the model, the category with the lowest value will be the reference category (i.e. No).

reg gpa bullied if pop_linear==1

R-squared is 0.01. Thus, bullied only explains 1% of the variance in gpa.

The B coefficient for bullied is -0.23. In other words, those who have been exposed to bullying have, on average, a 0.23 point lower grade point average compared to those who have not been exposed to bullying. This is not a very high estimate.

Nonetheless, there is a statistically significant association between bullied and gpa, as reflected by the p-value (0.000) and the 95% confidence interval (-0.27 to -0.18).

Summary At age 15, there is a negative (B=-0.23) and statistically significant (95% CI=-0.27 to -0.18) association between exposure to bullying and grade point average. Put differently, individuals who were exposed to bullying received a lower grade point average compared to those who were not exposed.