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The independent variable X from a linear regression is measured in miles. If you convert it to kilometres (keeping the unit of the dependent variable Y the same), how will the slope coefficient change? (Note: 1 mile = 1.6 km)It will get multiplied by 1.6.It will get divided by 1.6.It will remain the same.Cannot say.

Question

The independent variable X from a linear regression is measured in miles. If you convert it to kilometres (keeping the unit of the dependent variable Y the same), how will the slope coefficient change? (Note: 1 mile = 1.6 km)It will get multiplied by 1.6.It will get divided by 1.6.It will remain the same.Cannot say.

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Solution

The slope coefficient will get divided by 1.6. This is because when you convert miles to kilometers, you increase the number of units (since 1 mile = 1.6 km). In a linear regression, the slope coefficient represents the change in the dependent variable Y for a one-unit change in the independent variable X. So, if you increase the number of units of X by converting miles to kilometers, the amount of change in Y for a one-unit change in X will decrease, hence the slope coefficient will get divided by 1.6.

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