Question

Read the following description of a data set.
A selection of gemstones is showcased in the window of Oscar's jewelry store. Store managers wonder if showing a greater variety will encourage more people to enter the store.
The managers monitor other jewelry stores in town over one week. They note the number of gemstone types showcased at each store, x, as well as the number of people entering each store, y.
The least squares regression line of this data set is:
y=3.057x+137.126
How many people does this line predict will enter a jewelry store showcasing 9 types of gemstones?
Round your answer to the nearest integer.
customers

Answer 1

To predict the number of people entering a jewelry store showcasing 9 types of gemstones using the least squares regression line equation \( y = 3.057x + 137.126 \), we need to substitute \( x = 9 \) into the equation.

Calculating:

\[
y = 3.057(9) + 137.126
\]

First, compute \( 3.057 \times 9 \):

\[
3.057 \times 9 = 27.513
\]

Now add this value to 137.126:

\[
y = 27.513 + 137.126 = 164.639
\]

Rounding this to the nearest integer gives:

\[
\text{Predicted number of customers} = 165
\]

Thus, the regression line predicts that **165 customers** will enter a jewelry store showcasing 9 types of gemstones.