Question

A company sells name plates for doors. An employee takes a random sample of name plates, measures the length of each name (in inches), and counts the number of letters in each name. She generates the scatterplot and trend line equation shown below.



Name Plates
A graph has letters on the x-axis and length (inches) on the y-axis. A trend line goes through points (2, 4) and (9, 16). The regression equation is y = 1.75 x + 0.5.


A customer would like the company to build him a name plate that is 22 inches long. What is the best estimate of the number of letters the company can have on the name plate?
9
10
12
39

Answer 1

Use the regression y = 1.75x + 0.5 with y = 22:
22 = 1.75x + 0.5 → 1.75x = 21.5 → x = 21.5/1.75 ≈ 12.29.
Best estimate (whole letters) = 12.