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

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

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?

Answer 1

To find out how many errors would be made if the students typed zero words per minute, we can 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 that they would make approximately -155.317 errors. This doesn't make sense in the context of the problem since you cannot have a negative number of errors.

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

The coefficient of x in the regression line is 3.473, so 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 = 173.66 - 155.317
y ≈ 18.34

The regression line predicts that the student would make approximately 18.34 errors.

If a student types at 70 words per minute:

y = 3.473(70) - 155.317
y = 243.1 - 155.317
y ≈ 87.783

The regression line predicts that the student would make approximately 87.783 errors.

Overall, the data from the regression line does not support Mr. Moore's claim that the slower a student types, the fewer errors will be made. The regression line predicts that as typing speed increases, the number of errors made also increases at a rate of 3.473 errors per word per minute.