Mr. Moore is trying to convince his high school students that it is better to slow down when they are learning to type. He believes that students who type too quickly make too many errors. To prove this point, Mr. Moore has the students take a typing test. He records their average typing speed (in words per minute), x, and the number of errors they made, y.

Question

Mr. Moore is trying to convince his high school students that it is better to slow down when they are learning to type. He believes that students who type too quickly make too many errors. To prove this point, Mr. Moore has the students take a typing test. He records their average typing speed (in words per minute), x, and the number of errors they made, y.

The line of best fit/regression line of this data is:

y=3.473x−155.317
𝑦
=
3.473
𝑥
−
155.317
(5 points)
Using the regression line, about how many errors would be made if the students typed zero words per minute?

For an increase of one word per minute typing speed, the regression line predicts an increase of how many errors?

If a student types at 50 words per minute, how many errors does the regression line predict will be made?

If a student types 70 words per minute, how many errors does the regression line predict will be made?

Does this support Mr. Moore's claim that the slower a student types, the fewer errors will be made?

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1 answer
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Answer 1

Bot GPT 3.5 answered

To find the number of errors if the students typed zero words per minute, we substitute x=0 into the regression line:

y=3.473(0)-155.317
y=-155.317

Therefore, if the students typed zero words per minute, the regression line predicts they would make approximately -155 errors. However, since the number of errors cannot be negative, this value is not meaningful in this context.

For an increase of one word per minute typing speed, the regression line predicts an increase of 3.473 errors.

If a student types at 50 words per minute:
y=3.473(50)-155.317
y=173.65

The regression line predicts that the student would make approximately 173.65 errors.

If a student types at 70 words per minute:
y=3.473(70)-155.317
y=240.413

The regression line predicts that the student would make approximately 240.41 errors.

Based on the data and the regression line, it does support Mr. Moore's claim that the slower a student types, the fewer errors will be made. As typing speed increases, the regression line predicts that the number of errors also increases.