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
A. Using the regression line, about how many errors would be made if the students typed zero words per minute?
B. For an increase of one word per minute typing speed, the regression line predicts an increase of how many errors?
C. If a student types at 50 words per minute, how many errors does the regression line predict will be made?
D. If a student types 70 words per minute, how many errors does the regression line predict will be made?
E. Does this support Mr. Moore's claim that the slower a student types, the fewer errors will be made?
A. Using the regression line, about how many errors would be made if the students typed zero words per minute?
B. For an increase of one word per minute typing speed, the regression line predicts an increase of how many errors?
C. If a student types at 50 words per minute, how many errors does the regression line predict will be made?
D. If a student types 70 words per minute, how many errors does the regression line predict will be made?
E. Does this support Mr. Moore's claim that the slower a student types, the fewer errors will be made?
Answers
GPT-4o mini
To analyze Mr. Moore's regression line \( y = 3.473x - 155.317 \), we can answer each of the questions step by step.
### A. Using the regression line, about how many errors would be made if the students typed zero words per minute?
To find the predicted number of errors when the typing speed \( x = 0 \):
\[
y = 3.473(0) - 155.317 = -155.317
\]
This result does not make practical sense in the context of typing errors, as the number of errors cannot be negative, indicating that the model may not be valid at very low typing speeds.
### B. For an increase of one word per minute typing speed, the regression line predicts an increase of how many errors?
The slope of the regression line is \( 3.473 \). This means that for each increase of one word per minute in typing speed, the number of errors is predicted to increase by **3.473 errors**.
### C. If a student types at 50 words per minute, how many errors does the regression line predict will be made?
To find the predicted errors for \( x = 50 \):
\[
y = 3.473(50) - 155.317 = 173.65 - 155.317 = 18.333
\]
Thus, the regression line predicts that a student typing at 50 words per minute will make approximately **18 errors**.
### D. If a student types 70 words per minute, how many errors does the regression line predict will be made?
To find the predicted errors for \( x = 70 \):
\[
y = 3.473(70) - 155.317 = 243.11 - 155.317 = 87.793
\]
Therefore, the regression line predicts that a student typing at 70 words per minute will make approximately **88 errors**.
### E. Does this support Mr. Moore's claim that the slower a student types, the fewer errors will be made?
Mr. Moore's claim suggests that slower typing should result in fewer errors. However, the regression line shows a positive relationship between typing speed \( x \) and number of errors \( y \), meaning that as typing speed increases, the number of errors also increases.
Thus, the regression analysis **does not support Mr. Moore's claim**. Instead, it suggests that higher typing speeds lead to more errors according to the data modeled by the regression line.
### A. Using the regression line, about how many errors would be made if the students typed zero words per minute?
To find the predicted number of errors when the typing speed \( x = 0 \):
\[
y = 3.473(0) - 155.317 = -155.317
\]
This result does not make practical sense in the context of typing errors, as the number of errors cannot be negative, indicating that the model may not be valid at very low typing speeds.
### B. For an increase of one word per minute typing speed, the regression line predicts an increase of how many errors?
The slope of the regression line is \( 3.473 \). This means that for each increase of one word per minute in typing speed, the number of errors is predicted to increase by **3.473 errors**.
### C. If a student types at 50 words per minute, how many errors does the regression line predict will be made?
To find the predicted errors for \( x = 50 \):
\[
y = 3.473(50) - 155.317 = 173.65 - 155.317 = 18.333
\]
Thus, the regression line predicts that a student typing at 50 words per minute will make approximately **18 errors**.
### D. If a student types 70 words per minute, how many errors does the regression line predict will be made?
To find the predicted errors for \( x = 70 \):
\[
y = 3.473(70) - 155.317 = 243.11 - 155.317 = 87.793
\]
Therefore, the regression line predicts that a student typing at 70 words per minute will make approximately **88 errors**.
### E. Does this support Mr. Moore's claim that the slower a student types, the fewer errors will be made?
Mr. Moore's claim suggests that slower typing should result in fewer errors. However, the regression line shows a positive relationship between typing speed \( x \) and number of errors \( y \), meaning that as typing speed increases, the number of errors also increases.
Thus, the regression analysis **does not support Mr. Moore's claim**. Instead, it suggests that higher typing speeds lead to more errors according to the data modeled by the regression line.