Question

The owner of a restaurant would like to expand the menu but is concerned that this may detract from the quality of the food. Over the next few weeks, she varies the number of dishes on the menu and asks her customers to fill out comment cards.
Each week she notes the number of dishes offered, x, as well as the average customer satisfaction rating on a scale of 1 to 10, y, where 10 is excellent.
Dishes Rating
15 6
17 7
18 5
19 4
20 5
20 4
The least squares regression line of this data set is:
y=
–
0.434x+13.044
What average customer satisfaction rating does this line predict if 16 dishes are offered?
Round your answer to the nearest integer.

Answer 1

To predict the average customer satisfaction rating when 16 dishes are offered using the least squares regression line, we can substitute \(x = 16\) into the equation of the line:

\[
y = -0.434x + 13.044
\]

Substituting \(x = 16\):

\[
y = -0.434(16) + 13.044
\]

Calculating this step by step:

1. Calculate \(-0.434 \times 16\):

\[
-0.434 \times 16 = -6.944
\]

2. Now, add this to 13.044:

\[
y = -6.944 + 13.044 = 6.1
\]

To round this to the nearest integer:

\[
\text{Rounded } 6.1 \approx 6
\]

Therefore, the predicted average customer satisfaction rating when 16 dishes are offered is **6**.