High School

Consider the following sample regression equation \( y = 150 - 20x \), where \( y \) is the demand for Product A (in 1000s) and \( x \) is the price of the product (in \$).

If the price of the good increases by \$3, then we expect the demand for Product A to:

A. Decrease by 60
B. Decrease by 60000
C. Increase by 60
D. Increase by 60000

Answer :

The correct answer is: Decrease by 60.If the price of the good increases by $3, we expect the demand for Product A to decrease by 60 (in 1000s), as indicated in the first option.

The given regression equation is y = 150 - 20x, where y represents the demand for Product A (in 1000s) and x represents the price of the product (in $).

To find out the effect of a $3 increase in price on the demand for Product A, we substitute x = current price + $3 into the equation and calculate the corresponding value of y.

Let's consider the initial price to be p.

If the price increases by $3, the new price becomes p + $3.

Now, substitute x = p + $3 into the regression equation:

y = 150 - 20(p + $3)

Simplifying the equation:

y = 150 - 20p - 60

y = 90 - 20p

From the equation, it is evident that an increase in price leads to a decrease in demand. Therefore, if the price of the good increases by $3, we expect the demand for Product A to decrease by 60 (in 1000s), as indicated in the first option.

Hence, the correct answer is: Decrease by 60.

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