Question

4. We would prefer to estimate the number of books in a college library without counting them. Data are collected from colleges across Books (in millions)

Books (in millions)	Students Enrollment	Highest Degree	Area
4	5	3	20
5	8	3	40
10	40	3	100
1	4	2	50
0.5	2	1	300
2	8	1	400
7	30	3	40
4	20	2	200
1	10	2	5
1	12	1	100

Using Stepwise regression, show how each of the three factors affects the number of volumes in a college library.

Answer 1

The first regression output is:

	R²	0.966
	Adjusted R²	0.950
	R	0.983
	Std. Error	0.698
	n	10
	k	3
	Dep. Var.	Books (in millions)
ANOVA table
Source	SS	df	MS	F	p-value
Regression	84.3014	3	28.1005	57.67	.0001
Residual	2.9236	6	0.4873
Total	87.2250	9
Regression output					confidence interval
variables	coefficients	std. error	t (df=6)	p-value	95% lower	95% upper
Intercept	-4.9508
Students Enrollment	0.1420	0.0221	6.416	.0007	0.0878	0.1962
Highest Degree	2.6257	0.4286	6.126	.0009	1.5770	3.6744
Area	0.0081	0.0025	3.209	.0184	0.0019	0.0142

Since all the variables are significant, we can say that all of the three factors affects the number of volumes in a college library.

We can say all the variables are significant because all the p-values for the independent variables are less than 0.05.