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.
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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