Question

Q1. The following Regression function has been developed to check the relationship between the dependent variable y and the independent variable xz. Consider the following Minitab output and answer the questions. Regression Equation 9 = 0.86 + 0.65 x a) (Apt). Please fill out the Coefficients table appropriately. Coefficients Term Coef SE Coef T-Value P-Value VIF Constant 0 1.38 16.58 0.000 X1 0.231 7.00 0.000 1.00 b) (4pt). Please fill out the ANOVA table appropriately. Analysis of Variance Source DF SS MS F 2.12 2.12 Regression Error (iv) (v) 0.12 17.37 Total 9 3.10 c) Suppose that variables X and X; are added to the above model and the following regression analysis is obtained Regression Analysis: Y versus X1, X2, X3 The regression equation is 9 = 0.35 + 0.26 X, + 0.13 X, + 0.46X, Term Coef SE Coef T Constant 0.35 0.53 0.65 X1 (vi) 0.09 2.89 X2 (Vii) 0.138 0.942 X3 0.46 0.12 3.83 (4pt). Please fill out the above Coefficients table appropriately.

Answer 1

Ans :

Given regression equation

$\small \widehat{y}$= 0.86 + 0.65 x₁

Ingeneral regression equation line

$\small \widehat{y}$ = $\small \widehat{\beta _0}$ +$\small \widehat{\beta _1}$ * $\small x$

From the given regression equation

$\small \widehat{\beta _0}$ = 0.86

$\small \widehat{\beta _1}$ = 0.65

a) Coefficients

Term	Coef	SE Coef	T value	p value	VIF
Constant	0.86	1.38	16.58	0.000
x1	0.65	0.231	7	0.000

Ans b) :

One way ANOVA

Source	DF	SS	MS	F
regression	k	SSregression	SSTreatment /k	MSTreatment/MSError
Error	n-k-1	SSError	SSError /n-k-1
Total	in-1	SSTotal

Now to calculate missing values

1)we know that MS_reg = SS_reg/df_reg

$\small \Rightarrow$degrees of freedom of regression =SS_reg/ MS_reg = 2.12/2.12 =1

2)degrees of freedom of error = df total -df of regression =9-1 = 8

3)SSE = SST -SS_regression = 3.10-2.12 =

Source	DF	SS	MS	F
regression	1	2.12	2.12	17.37
Error	8	0.98	0.12
Total	9	3.10

c) Ans :

Given regression equation :

$\small \widehat{y}$ = 0.35+0.26X₁ + 0.13X₂ +0.46X₃

Term	Coef	SE Coef	T
Constant	0.35	0.53	0.65
X1	0.26	0.09	2.89
X2	0.1	0.138	0.943
X3	0.46	0.12	3.83

d) ans :

ANOVA Table

Source	DF	SS	MS	F
regression	k	SSregression	SSTreatment /k	MSTreatment/MSError
Error	n-k-1	SSError	SSError /n-k-1
Total	in-1	SSTotal

Calculate missing values in given ANOVA table

1)SSE = SST -SS_regression 3.11 - 2.75 = 0.36

2) we know that MS_Error =SS_Error/df

$\small \Rightarrow$ df error = SS_Error / MS_Error = 0.36/0.06 = 6

3)df regression = k = 3

4) df total = df regression +df error = 6+3 = 9

5) MS_Treatment = 2.75/3 = 0.9166

6) F = 0.9166/0.06 = 15.2766

ANOVA Table

Source	DF	SS	MS	F
regression	3	2.75	0.9166	15.2766
Error	6	0.36	0.06
Total	9	3.11