Table 1.

Variable setting description.

Variable type	Variable name	Variable description
Dependent variable	Cognitive development	With the student achievement agent, the Elementary school grade is the average of the 2 courses of language and mathematics; the middle school grade is the average of the 6 courses of language, mathematics, English, physics, biology, and geography
Independent variable	Breakfast frequency	The number of days of breakfast in a week, 1–7 days, respectively
	Do not eat breakfast	1=breakfast irregularly (skip breakfast at least one day a week), 0= eat breakfast every day in the week
Control cariable	Family characteristics
	Student family socioeconomic status	The calculation of family socioeconomic status uses the 3 indicators of parental education, parental occupation, and family economic background to conduct Principal Component Analysis and convert it into a numerical value between 0 and 100
	Student characteristics
	Student gender	1=Male; 0=Female, dummy variable, “girl” is the control group
	Is it an only child?	1=Yes; 0=No, dummy variable, “non-only child” is the control group
	School characteristics
	Type of school area	Divided into rural, county, urban, dummy variables, “rural” as a control group

1. The socioeconomic status of the students’ families was calculated as follows: First, the education level of the parents is calculated according to the education information of the parents in the questionnaire, and the family economic status is calculated by the household facilities and durable consumer goods data in the questionnaire. The relevant literature is assigned [28,29]. Second, the original data is normalized, and the calculation method is: K_i=(X_i–X_min)/(X_max–X_min) where K is an index The standard value, X, is the original value of the indicator, X_min is the minimum value of the indicator, X _max is the maximum value of the indicator, i represents each sample, and the principal component method is used to weight each indicator to obtain the weight, w_i, and $\text{INDEX}={\sum }_{\text{i}=1}^{\text{n}}{\text{w}}_{\text{i}}\hspace{0.17em}{\text{k}}_{\text{i}}$ calculate the family background score for each sample, and multiply the calculated result by 100 to convert to value between 0 and 100.

2. Jiangsu Province is a province with relatively large internal differences. From an economic and cultural perspective, people are used to dividing Jiangsu into 3 regions: Northern Jiangsu, Central Jiangsu, and Southern Jiangsu. In order to control the socioeconomic background of the school’s region, we divided the school’s area into 3 regions: Northern Jiangsu, Central Jiangsu, and Southern Jiangsu.