The Simple Linear Regression model is       Y = b0 + b1*X1 + u       and the Multiple Linear Regression model with k variables is:       Y = b0 + b1*X1 + b2*X2 + ... + bk*Xk + u       Y is the dependent variable, the X1, X2, ..., Xk are the explanatory variables, b0 is the intercept, b1, b2, ..., bk are the slope coefficients, and u is the error term,       Yhat represents the OLS fitted values, uhat represent the OLS residuals, b0_hat represents the OLS estimated intercept, and b1_hat, b2_hat,..., bk_hat, represent the OLS estimated slope coefficients. QUESTION 7 In the MLR model, the assumption of ‘linearity in parameters’ is violated if:   one of the slope coefficients appears as a power (e.g. Y = b0 + b1*(X1^b2) + b3*X2 + u) the model includes the reciprocal of a variable (e.g. 1/X1) the model includes a variable squared (e.g. X1^2) the model includes a variable in its logarithmic form (i.e. log(X1) )     QUESTION 8 In the MLR model, the assumption of 'no perfect collinearity' is violated if:    the model includes two variables that are not correlated the model includes both X1 and X1^2 (i.e. X1-squared) if two of the explanatory variables have a Pearson correlation equal to 0.98 if two of the explanatory variables have a Pearson correlation equal to -1     QUESTION 9 Suppose the estimated MLR model is, Yhat = 2 + 1.5*X1 + 0.5*X2 + 2*X3. Suppose that for an observation with X1=2, X2=-2, X3=5, we observe an actual value in the sample of Y=10. What is the residual, uhat, for this observation?   negative 4 negative 14 positive 4 positive 14

MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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The Simple Linear Regression model is
 
 
 
Y = b0 + b1*X1 + u
 
 
 
and the Multiple Linear Regression model with k variables is:
 
 
 
Y = b0 + b1*X1 + b2*X2 + ... + bk*Xk + u
 
 
 
Y is the dependent variable, the X1, X2, ..., Xk are the explanatory variables, b0 is the intercept, b1, b2, ..., bk are the slope coefficients, and u is the error term,
 
 
 
Yhat represents the OLS fitted values, uhat represent the OLS residuals, b0_hat represents the OLS estimated intercept, and b1_hat, b2_hat,..., bk_hat, represent the OLS estimated slope coefficients.

QUESTION 7

In the MLR model, the assumption of ‘linearity in parameters’ is violated if:

 

  1. one of the slope coefficients appears as a power (e.g. Y = b0 + b1*(X1^b2) + b3*X2 + u)
  2. the model includes the reciprocal of a variable (e.g. 1/X1)
  3. the model includes a variable squared (e.g. X1^2)
  4. the model includes a variable in its logarithmic form (i.e. log(X1) )

 

 

QUESTION 8

In the MLR model, the assumption of 'no perfect collinearity' is violated if: 

 

  1. the model includes two variables that are not correlated
  2. the model includes both X1 and X1^2 (i.e. X1-squared)
  3. if two of the explanatory variables have a Pearson correlation equal to 0.98
  4. if two of the explanatory variables have a Pearson correlation equal to -1

 

 

QUESTION 9

Suppose the estimated MLR model is, Yhat = 2 + 1.5*X1 + 0.5*X2 + 2*X3.

Suppose that for an observation with X1=2, X2=-2, X3=5, we observe an actual value in the sample of Y=10. What is the residual, uhat, for this observation?

 

  1. negative 4
  2. negative 14
  3. positive 4
  4. positive 14

 

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