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
(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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Answer 1

To find the predicted number of errors when the students type zero words per minute, we can plug in x=0 into the regression equation:

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

Therefore, the predicted number of errors when typing zero words per minute is -155.317. This may not be a meaningful interpretation since typing zero words per minute is not practical.

For an increase of one word per minute typing speed, the regression line predicts an increase of 3.473 errors. This means that for each additional word per minute typed, the number of errors is predicted to increase by 3.473.

If a student types at 50 words per minute, we can plug x=50 into the regression equation:

y = 3.473(50) - 155.317
y = 173.65

So, the regression line predicts that a student typing at 50 words per minute will make approximately 173.65 errors.

If a student types at 70 words per minute, we can plug x=70 into the regression equation:

y = 3.473(70) - 155.317
y = 245.502

The regression line predicts that a student typing at 70 words per minute will make approximately 245.502 errors.

Based on the regression equation, it does not directly support Mr. Moore's claim that the slower a student types, the fewer errors will be made. The regression line shows that as typing speed increases, the number of errors also increases. However, it does not provide direct evidence that slowing down while typing results in fewer errors, as it only shows a correlation between typing speed and errors made.