The Simple Linear Regression model is Y = b0 + b1X1 + u and the Multiple Linear Regression model with k variables is: Y = b0 + b1X1 + b2X2 + ... + bkXk + 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) + b3X2 + 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 + 1.5X1 + 0.5X2 + 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

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter2: Matrices

Section2.CR: Review Exercises

Problem 90CR

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Related questions

Question

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?