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?
-155.317
For an increase of one word per minute typing speed, the regression line predicts an increase of how many errors?
3.473
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?
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?
-155.317
For an increase of one word per minute typing speed, the regression line predicts an increase of how many errors?
3.473
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?
Answers
GPT-4o mini
To find the predicted number of errors for a student typing at 50 words per minute and at 70 words per minute using the regression line equation \( y = 3.473x - 155.317 \), we can substitute the values of \( x \) into the equation.
1. **For a student typing at 50 words per minute:**
\[
y = 3.473(50) - 155.317
\]
\[
y = 173.65 - 155.317
\]
\[
y \approx 18.333
\]
So, the regression line predicts that a student typing at 50 words per minute will make about **18.33 errors**.
2. **For a student typing at 70 words per minute:**
\[
y = 3.473(70) - 155.317
\]
\[
y = 243.11 - 155.317
\]
\[
y \approx 87.793
\]
Thus, the regression line predicts that a student typing at 70 words per minute will make about **87.79 errors**.
### Support for Mr. Moore's Claim:
Mr. Moore's claim is that slower typing is associated with fewer errors.
- At 50 words per minute, the predicted errors are approximately 18.33.
- At 70 words per minute, the predicted errors are approximately 87.79.
The increase in errors from typing at 50 to 70 words per minute (from ~18.33 to ~87.79) indicates that typing more quickly (as in the case of 70 wpm) leads to a significantly higher number of errors.
This supports Mr. Moore's claim that the slower a student types, the fewer errors they will make, as the number of predicted errors increases with increased typing speed according to the regression line.
1. **For a student typing at 50 words per minute:**
\[
y = 3.473(50) - 155.317
\]
\[
y = 173.65 - 155.317
\]
\[
y \approx 18.333
\]
So, the regression line predicts that a student typing at 50 words per minute will make about **18.33 errors**.
2. **For a student typing at 70 words per minute:**
\[
y = 3.473(70) - 155.317
\]
\[
y = 243.11 - 155.317
\]
\[
y \approx 87.793
\]
Thus, the regression line predicts that a student typing at 70 words per minute will make about **87.79 errors**.
### Support for Mr. Moore's Claim:
Mr. Moore's claim is that slower typing is associated with fewer errors.
- At 50 words per minute, the predicted errors are approximately 18.33.
- At 70 words per minute, the predicted errors are approximately 87.79.
The increase in errors from typing at 50 to 70 words per minute (from ~18.33 to ~87.79) indicates that typing more quickly (as in the case of 70 wpm) leads to a significantly higher number of errors.
This supports Mr. Moore's claim that the slower a student types, the fewer errors they will make, as the number of predicted errors increases with increased typing speed according to the regression line.