Consider the following model: YIELDi = B1 + B2 x RAINFALL + ui Yield is measured...

Consider the following model: YIELDi = B1 + B2 x RAINFALL + ui

Yield is measured in tons per acre and rainfall is measured in liters. Answer the questions:

What would happen to the value of B1 and of B2 if yield were to be measured in kilograms (kg) per acre instead of tons (1 ton = 1,000 kg). Rainfall is still measured in liters.
What would happen to the value of B1 and of B2 if rainfall were to be measured in milliliters instead of liters (1 liter = 1,000 ml). Yield would still be in tons per acre.
What would happen to the value of B1 and of B2 if rainfall were to be measured in milliliters instead of liters (1 liter = 1,000 ml) at the same time as yield being measured in kilograms (kg) per acre instead of tons (1 ton = 1,000 kg)

Expert Solution

ANSWER::

1). To measure the accurate scale of Y in kgs (where 1 ton = 1000 kgs), coefficients will be multiplied by 1000.

1'= 1 * 1000 and 2'= 2 * 1000.

2). To measure the accurate scale when Y is in tons but X's change from litres to mililiters ( 1 litre = 1000 mililitre), coefficients will be divided by 1000.

1'= 1 / 1000 and 2'= 2 /1000.

3.) When Y changes from ton to kgs and X's changes from litre to mililitres (s.t., 1 ton = 1000 kgs and 1 litre = 1000 mililitre), then coefficients remain the same.

1'= 1 and 2'= 2

where 1' and 2' are the new or transformed coefficients.

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orchestra answered 2 years ago

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