Question

In: Math

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


Related Solutions

Fit a multiple linear regression model of the form y=β0 + β1 x1 + β2 x2...
Fit a multiple linear regression model of the form y=β0 + β1 x1 + β2 x2 + β3 x3 + ε. Here, ε is the random error term that is assumed to be normally distributed with 0 mean and constant variance. State the estimated regression function. How are the estimates of the three regression coefficients interpreted here? Provide your output, and interpretations in a worksheet titled “Regression Output.” Obtain the residuals and prepare a box-plot of the residuals. What information...
When we estimate a linear multiple regression model (including a linear simple regression model), it appears...
When we estimate a linear multiple regression model (including a linear simple regression model), it appears that the calculation of the coefficient of determination, R2, for this model can be accomplished by using the squared sample correlation coefficient between the original values and the predicted values of the dependent variable of this model. Is this statement true? If yes, why? If not, why not? Please use either matrix algebra or algebra to support your reasoning.
Discuss the underlying assumptions of a simple linear regression model; multiple regression model; and polynomial regression.
Discuss the underlying assumptions of a simple linear regression model; multiple regression model; and polynomial regression.
Estimate the multiple linear regression equation     for the given data    1              2        &n
Estimate the multiple linear regression equation     for the given data    1              2              3               4 10             1              2               3 12            18            24             30 Estimate the multiple linear regression equation y with overparenthesis on top equals b subscript 0 plus b subscript 1 x subscript 1 plus b subscript 2 x subscript 2 for the given data x subscript 1 1 2 3 4 x subscript 2 10 1 2 3 y 12 18 24 30
Lets say Y=a+bX1+cX2+dX3+.......................up to n.....is the regression model (1) What would be the X1,X2,X3........Xn predictors for...
Lets say Y=a+bX1+cX2+dX3+.......................up to n.....is the regression model (1) What would be the X1,X2,X3........Xn predictors for house price in your neighborhood. Discuss from most important predictor to least important predictor. (2) Similarly, What would be the predictors of your salary? Discuss in order.
Lets say Y=a+bX1+cX2+dX3+.......................up to n.....is the regression model (1) What would be the X1,X2,X3........Xn predictors for...
Lets say Y=a+bX1+cX2+dX3+.......................up to n.....is the regression model (1) What would be the X1,X2,X3........Xn predictors for house price in your neighborhood. Discuss from most important predictor to least important predictor. (2) Similarly, What would be the predictors of your salary? Discuss in order.
The following is the estimation results for a multiple linear regression model: SUMMARY OUTPUT             Regression...
The following is the estimation results for a multiple linear regression model: SUMMARY OUTPUT             Regression Statistics R-Square                                                       0.558 Regression Standard Error (S)                  863.100 Observations                                               35                                Coeff        StdError          t-Stat    Intercept               1283.000    352.000           3.65    X1                             25.228        8.631                       X2                               0.861        0.372           Questions: Interpret each coefficient.
The following is the estimation results for a multiple linear regression model: SUMMARY OUTPUT             Regression...
The following is the estimation results for a multiple linear regression model: SUMMARY OUTPUT             Regression Statistics R-Square                                                       0.558 Regression Standard Error (S)                  863.100 Observations                                               35                                Coeff        StdError          t-Stat    Intercept               1283.000    352.000           3.65    X1                             25.228        8.631                       X2                               0.861        0.372           Question: 1. A. Write the fitted regression equation. B. Write the estimated intercepts and slopes, associated with their corresponding standard errors. C. Interpret each coefficient.
1. A multiple linear regression model should not be used if: A The variables are all...
1. A multiple linear regression model should not be used if: A The variables are all statistically significant. B The coefficient of determination R2 is large. C Both of the above. D Neither of the above. 2. Consider a multiple linear regression model where the output variable is a company's revenue for different months, and the purpose is to investigate how the revenue depends upon the company's advertising budget. The input variables can be time-lagged so that the first input...
for stat students, model ( linear regression, multiple regression,factorial experiments,liner model) for each statistical method ,...
for stat students, model ( linear regression, multiple regression,factorial experiments,liner model) for each statistical method , why is the underlying statistical model important ? more than 4 reasons. please explain in clear way , i will discuss that with my class . Thx
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT