True or False _____I. If a negative correlation exists between X and Y, and a new...

True or False

_____I. If a negative correlation exists between X and Y, and a new data point is added whose Z_X = -2.5 and Z_Y = 2.5, |r| will decrease.

_____J. If a positive correlation exists between X and Y, and a new data point is added whose Z_X = 2.5 and Z_Y = 2.5, |r| will decrease.

_____K. In simple linear regression predicting Y from X, the unstandardized coefficient of the X variable will always equal the Pearson r between X and Y. (Assume X and Y are not measured as z scores.)

_____L. In simple linear regression predicting Y from X, the standardized coefficient of the X variable will always equal the Pearson r between X and Y.

_____M. In multiple regression predicting Y from two X variables, the standardized coefficient for the first X variable will always equal the Pearson r between that X and Y.

Solutions

Expert Solution

_____I. If a negative correlation exists between X and Y, and a new data point is added whose Z_X = -2.5 and Z_Y = 2.5, |r| will decrease.

Since Z_X = -2.5 and Z_Y = 2.5 are of opposite signs and absolute value is greater than 2, the absolute value of negative correlation will increase. The statement is False.

_____J. If a positive correlation exists between X and Y, and a new data point is added whose Z_X = 2.5 and Z_Y = 2.5, |r| will decrease.

Since Z_X = 2.5 and Z_Y = 2.5 are of same signs and absolute value is greater than 2, the absolute value of positive correlation will increase. The statement is False.

In simple linear regression predicting Y from X, the standardized coefficient of the X variable will always equal the Pearson r between X and Y. The statement is False.

_____L. In simple linear regression predicting Y from X, the standardized coefficient of the X variable will always equal the Pearson r between X and Y.

In simple linear regression predicting Y from X, the standardized coefficient of the X variable will always equal the Pearson r between X and Y. The statement is True.

_____M. In multiple regression predicting Y from two X variables, the standardized coefficient for the first X variable will always equal the Pearson r between that X and Y.

In multiple regression predicting Y from two X variables, the standardized coefficient for the first X variable will always equal the partial r between that X and Y. The statement is False.

milcah answered 8 months ago

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