Question

Source	df	SS	MS	F	Significance of F
Regression		207 (Given)
Residual			16.59 (Given)
Total

Suppose that a multiple regression model was developed with a sample of data of size 190 and 13 independent variables. One of the 13 independent variables is a qualtiative variable with 6 levels for which necessary dummy variables were defined.

a)

The following is a partially complete ANOVA table for the Multiple Regression analysis. Round Answer to 4 Decimal Places

Answer 1

Here, we have to complete the ANOVA table.

We are given

Total number of independent variables = 13

We know, number of dependent variable = 1

Out of 13 independent variables, 12 are quantitative and 1 is qualitative.

1 qualitative variable have 6 levels. So, we need to define 6 dummy variables for this qualitative variable.

After defining 6 dummy variables, total independent variables are 12+6 = 18 variables.

Now, we have 18 independent + 1 dependent = 19 variables.

Regression df = 19 – 1 = 18

We are given N = 190

So, total df = N – 1 = 190 – 1 = 189

Residual df = total df – regression df = 189 – 18 = 171

MS = SS/df

MS regression = 207/18 = 11.5

SS = df*MS

SS residual = 171*16.59 = 2836.89

F = MS regression / MS residual

F = 11.5/16.59

F = 0.693188668

P-value or significance of F = 0.81487726

(By using F-table or excel)

Required ANOVA table is given as below:

Source	df	SS	MS	F	Significance of F
Regression	18	207	11.5	0.693188668	0.81487726
Residual	171	2836.89	16.59
Total	189	3043.89