Question

Determine if the addition of the extra variables significantly improves the model’s ability to explain the variance in the dependent variables. Show your work.

2-Variables (R² = 0.4452)

	SS	df	MS	F
Model	2602.72	2	1301.36	5648.45
Residual	3243.14	13,628	0.24

6-Variables (Add 4) (R² = 0.4500)

	SS	df	MS	F
Model	2630.60	6	438.44	1857.77
Residual	3215.26	13,624	0.24

Answer 1

When model includes only two variables,

R-square = 44.52%

This model explains 44.52% of the variation with 2 variales.

And F-stat = 5648.45

F-table value = F(2, 13628) = 2.996

Hence, model is statistically significant.

When model includes only Six variables,

R-square = 45.00%

This model explains 45% of the variation with 6 varibles (With addition of 4 more variables).

And F-stat = 1857.77

F-table value = F(6, 13624) = 2.409

Hence, model is statistically significant.

Actually, there is not much difference in the variation explained by increasing 4 more variables.

Hence, addition of the more variables does not actually improves the model significance.