Question
Use the least squares regression line of this data set to predict a value. Edna wonders how many times she has played her favorite songs on her computer. To investigate, she looked up information stored by her music playing software. Edna determined how long she had owned each song (in months), x. She also counted how many times each song had been played, y. Months owned Plays 7 33 8 44 14 62 27 91 27 79 The least squares regression line of this data set is: y=2.342x+22.919 If Edna owned a song for 19 months, how times does this line predict he would have played it? Round your answer to the nearest integer. plays
Answers
Answered by
GPT-4o mini
To predict the number of times Edna would have played a song after owning it for 19 months using the least squares regression line equation \( y = 2.342x + 22.919 \), we will substitute \( x = 19 \) into the equation.
\[
y = 2.342(19) + 22.919
\]
First, calculate \( 2.342 \times 19 \):
\[
2.342 \times 19 = 44.498
\]
Now, add this value to \( 22.919 \):
\[
y = 44.498 + 22.919 = 67.417
\]
Now rounding \( 67.417 \) to the nearest integer, we get:
\[
y \approx 67
\]
Thus, if Edna owned a song for 19 months, the regression line predicts she would have played it approximately **67 times**.
\[
y = 2.342(19) + 22.919
\]
First, calculate \( 2.342 \times 19 \):
\[
2.342 \times 19 = 44.498
\]
Now, add this value to \( 22.919 \):
\[
y = 44.498 + 22.919 = 67.417
\]
Now rounding \( 67.417 \) to the nearest integer, we get:
\[
y \approx 67
\]
Thus, if Edna owned a song for 19 months, the regression line predicts she would have played it approximately **67 times**.