Question

Use the least squares regression line of this data set to predict a value.
Zachary wonders how many times he has played his favorite songs on his computer. To investigate, he looked up information stored by his music playing software.
Zachary determined how long he had owned each song (in months), x. He also counted how many times each song had been played, y.
Months owned Plays
6 32
10 57
12 56
17 58
26 87
28 81
The least squares regression line of this data set is:
y=2.095x+27.269
If Zachary owned a song for 20 months, how times does this line predict he would have played it?
Round your answer to the nearest integer.
plays

Answer 1

To predict how many times Zachary would have played a song he has owned for 20 months, we can substitute \( x = 20 \) into the least squares regression line equation \( y = 2.095x + 27.269 \).

Substituting in the values, we get:

\[
y = 2.095(20) + 27.269
\]

Calculating this step-by-step:

1. Calculate \( 2.095 \times 20 \):
\[
2.095 \times 20 = 41.9
\]

2. Now add 27.269:
\[
41.9 + 27.269 = 69.169
\]

Rounding to the nearest integer gives us:

\[
y \approx 69
\]

Therefore, the prediction for how many times Zachary would have played a song owned for 20 months is **69 plays**.