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In a multiple linear regression model with 2 predictors (X1and X2),                               &n

In a multiple linear regression model with 2 predictors (X1and X2),                                TRUE     or     FALSE

In a multiple linear regression model with 2 predictors (X1and X2), then SSR(X1)+SSR(X2|X1) = SSTO–SSE(X1,X2)   TRUE     or    FALSE

In a multiple linear regression model with 2 predictors (X1and X2), if X1and X2are uncorrelated, SSR(X1) = SSR(X1|X2).       TRUE     or    FALSE

In a multiple linear regression model with 2 predictors (X1and X2), SSR(X1) + SSR(X2|X1) = SSR(X2) + SSR(X1|X2).       TRUE     or    FALSE

In simple linear regression, then (X’X)-1is  2x2.    TRUE    or     FALSE

In simple linear regression, the hat-matrix is 2x2.    TRUE    or     FALSE

Solutions

Expert Solution

-> In a multiple linear regression model with 2 predictors (X1and X2), then SSR(X1)+SSR(X2|X1) = SSTO–SSE(X1,X2)

For Multiple Linear Regression Equation:

SSTO = SSR(X1, X2) + SSE(X1, X2) -------------- (1)

Now,

SSR(X2|X1) = SSR(X1, X2) − SSR(X1) =>  SSR(X1, X2) = SSR(X2|X1) + SSR(X1)

Putting in (1) we get

SSTO = SSR(X2|X1) + SSR(X1) + SSE(X1, X2)

=> SSTO = SSR(X2|X1) + SSR(X1) + SSE(X1, X2)

=> SSTO -  SSE(X1, X2) = SSR(X2|X1) + SSR(X1)

Hence Above statement is True

-> In a multiple linear regression model with 2 predictors (X1and X2), if X1and X2 are uncorrelated, SSR(X1) = SSR(X1|X2)

Consider the 3 models: (1) E(Yi) = bo + b1Xi1

(2) E(Yi) = bo + b2Xi2

(3) E(Yi) = b0 + b1Xi1 + b2Xi2

X1 and X2 are uncorrelated (r12 ≈ 0), then

-> b1 will be the same for models (1) and (3)

-> b2 will be the same for models (2) and (3)

SSR(X1|X2) = SSR(X1) and

SSR(X2|X1) = SSR(X2)

Hence Above Statement is True

-> In a multiple linear regression model with 2 predictors (X1and X2), SSR(X1) + SSR(X2|X1) = SSR(X2) + SSR(X1|X2).

As we knor that:

SSR(X2|X1) = SSR(X1, X2) − SSR(X1) --------------- (1)

SSR(X1|X2) = SSR(X1, X2) − SSR(X2) --------------- (2)

Subtracting (2) from (1) we get,

SSR(X2|X1) - SSR(X1|X2) = − SSR(X1) +  SSR(X2)

SSR(X2|X1) + SSR(X1) = SSR(X1|X2) + SSR(X2)

Hence above statement is True

->In simple linear regression, then (X’X)-1 is  2x2.

TRUE

-> In simple linear regression, the hat-matrix is 2x2

FALSE

milcah answered 11 months ago
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