Question

market researchers were interested in the relationship between the number of pieces in a brick - building set and the cost of the set. information was collected from a survey and was used to obtain the regression equation $\hat{y}=0.08x + 1.20$, where $x$ represents the number of pieces in a set and $\hat{y}$ is the predicted price (in dollars) of a set. what is the predicted price of a set that has 500 pieces?\
\bigcirc $40\
\bigcirc $41.20\
\bigcirc $600\
\bigcirc $6,235

Explanation:

Step1: Identify the values

We know that the regression equation is \( y = 0.08x + 1.20 \), and \( x = 500 \) (the number of pieces).

Step2: Substitute x into the equation

Substitute \( x = 500 \) into \( y = 0.08x + 1.20 \):
\( y = 0.08\times500 + 1.20 \)

Step3: Calculate the multiplication

First, calculate \( 0.08\times500 \):
\( 0.08\times500 = 40 \)

Step4: Calculate the addition

Then, add \( 1.20 \) to the result:
\( y = 40 + 1.20 = 41.20 \)

Answer:

\$41.20