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Use the least squares regression line of this data set to predict a value.Playing video games makes Francesca so happy that she thinks it even helps her complete more schoolwork. Francesca's roommate Justine is skeptical, so over the next few days, Justine asks Francesca about her progress on her daily reading.For each day, Justine notes the number of minutes Francesca spends playing video games, x. She also takes the number of pages Francesca reads and divides it by the total number of pages assigned, y.Minutes playing video games Percentage of reading assignment103 59.56111 54.57112 35.28112 57.78117 32.95The least squares regression line of this data set is:y=–1.821x+250.135If Francesca spends 109 minutes playing video games, what percentage of her daily reading assignment does this line predict she will complete?Round your answer to the nearest thousandth. percent

Question

Use the least squares regression line of this data set to predict a value.Playing video games makes Francesca so happy that she thinks it even helps her complete more schoolwork. Francesca's roommate Justine is skeptical, so over the next few days, Justine asks Francesca about her progress on her daily reading.For each day, Justine notes the number of minutes Francesca spends playing video games, x. She also takes the number of pages Francesca reads and divides it by the total number of pages assigned, y.Minutes playing video games Percentage of reading assignment103 59.56111 54.57112 35.28112 57.78117 32.95The least squares regression line of this data set is:y=–1.821x+250.135If Francesca spends 109 minutes playing video games, what percentage of her daily reading assignment does this line predict she will complete?Round your answer to the nearest thousandth. percent

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Solution

To predict the percentage of the daily reading assignment Francesca will complete, we need to substitute the value of x (minutes playing video games) into the equation of the least squares regression line.

The equation is: y = -1.821x + 250.135

Substitute x = 109 into the equation:

y = -1.821(109) + 250.135 y = -198.689 + 250.135 y = 51.446

So, if Francesca spends 109 minutes playing video games, the line predicts she will complete approximately 51.446% of her daily reading assignment. Rounded to the nearest thousandth, this is 51.446%.

This problem has been solved

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