Multiple Regression Analysis of student income on feeding and school expenses by Aniakor Blessing

The data blow shows the student income and expenses in feeding and school.

Multiple Regression of the student income on school and feeding expenses.

Summary statistics:

Variable	Observations	Obs. with missing data	Obs. without missing data	Minimum	Maximum	Mean	Std. deviation
Income	24	0	24	738.000	1199.000	990.792	142.948
Feeding Expenses	24	0	24	121.000	190.000	156.333	17.731
School Expenses	24	0	24	82.000	297.000	205.708	68.808


Correlation matrix:

	Feeding Expenses	School Expenses	Income
Feeding Expenses	1	-0.060	0.162
School Expenses	-0.060	1	-0.330
Income	0.162	-0.330	1


Multicolinearity statistics:

	Feeding Expenses	School Expenses
Tolerance	0.996	0.996
VIF	1.004	1.004


Regression of variable Income:

Goodness of fit statistics (Income):

Observations	24.000
Sum of weights	24.000
DF	21.000
R²	0.129
Adjusted R²	0.046
MSE	19495.066
RMSE	139.625
MAPE	11.625
DW	2.451
Cp	3.000
AIC	239.865
SBC	243.399
PC	1.120

Analysis of variance (Income):

Source	DF	Sum of squares	Mean squares	F	Pr > F
Model	2	60589.573	30294.786	1.554	0.235
Error	21	409396.385	19495.066
Corrected Total	23	469985.958
Computed against model Y=Mean(Y)


Model parameters (Income):

Source	Value	Standard error	t	Pr > \|t\|	Lower bound (95%)	Upper bound (95%)
Intercept	948.575	277.911	3.413	0.003	370.627	1526.522
Feeding Expenses	1.148	1.645	0.698	0.493	-2.273	4.569
School Expenses	-0.667	0.424	-1.574	0.130	-1.549	0.214


Equation of the model (Income):

Income = 948.574558731944+1.14800537969527Feeding Expenses-0.667228194082094School Expenses


Standardized coefficients (Income):

Source	Value	Standard error	t	Pr > \|t\|	Lower bound (95%)	Upper bound (95%)
Feeding Expenses	0.142	0.204	0.698	0.493	-0.282	0.567
School Expenses	-0.321	0.204	-1.574	0.130	-0.745	0.103

Interpretation (Income):

Given the R2, 13% of the variability of the dependent variable Income is explained by the 2 explanatory variables.


Given the p-value of the F statistic computed in the ANOVA table, and given the significance level of 5%, the information brought by the explanatory variables is not significantly better than what a basic mean would bring. The fact that variables do not bring significant information to the model may be interpreted in different ways: Either the variables do not contribute to the model, or some covariates that would help explaining the variability are missing, or the model is wrong, or the data contain errors.