A multiple regression model has the form y =b0+b1x1+b2x2y^=b0+b1x1+b2x2 The coef

Question

A multiple regression model has the form

y =b0+b1x1+b2x2y^=b0+b1x1+b2x2

The coefficient b1b1 is interpreted as the:
A. change in yy per unit change in x1x1
B. change in yy per unit change in x1x1, when x1x1 and x2x2 values are correlated
C. change in yy per unit change in x1x1, holding x2x2 constant
D. change in the average value of yy per unit change in x1x1, holding x2x2 constant

If multicollinearity exists among the independent variables included in a multiple regression model, the:
A. multiple coefficient of determination will assume a value close to zero
B. standard errors of the regression coefficients for the correlated independent variables will increase
C. regression coefficients will be difficult to interpret
D. regression coefficients will be difficult to interpret and the standard errors of the regression coefficients for the correlated independent variables will increase

Explanation / Answer

Ans:

1)Option D is correct.

change in the average value of y per unit change in x1, holding x2 constant

Explanation:

Regression coefficients represent the mean change in the response variable for one unit of change in the predictor variable while holding other predictors in the model constant.

2)

Option D is correct.

regression coefficients will be difficult to interpret and the standard errors of the regression coefficients for the correlated independent variables will increase

Explanation:

multicollinearity:When there are near-linear dependencies among the regressors, the problem of multicollinearity issaid to exist. Multicollinearity is a case of multiple regression in which the predictor variables are themselves highly correlated.

If the goal is simply to predict Y from a set of X variables, then multicollinearity is not a problem. The predictions will still be accurate, and the overall R2 (or adjusted R2 ) quantifies how well the model predicts the Y values.

If the goal is to understand how the various X variables impact Y, then multicollinearity is a big problem.

One problem is that the individual P values can be misleading (a P value can be high, even though the variable is important).

The second problem is that the confidence intervals on the regression coefficients will be very wide. The confidence intervals may even include zero, which means one can’t even be confident whether an increase in the X value is associated with an increase, or a decrease, in Y. Because the confidence intervals are so wide, excluding a subject (or adding a new one) can change the coefficients dramatically and may even change their signs

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