Question

Practice (hours) 1 2 3 4 5 6 Typing Speed (words per minute) 21 26 35 37 40 ?

a.y = 4.9x + 17.1; r = 0.971; about 47 words per minute
b.y = 17.1x + 4.9; r = 0.791; about 142 words per minute
c.y = 4.6x + 16; r = 0.902; about 53 words per minute
d.y = 5.1x + 17; r = 0.971; about 47 words per minute

Answer 1

To find the typing speed after 6 hours of practice, we examine the provided linear regression equations and their correlation coefficients, aiming for a high r value. Options a and d both predict 47 words per minute with a high correlation of 0.971, indicating a strong linear relationship between practice hours and typing speed.

Step-by-step explanation:

The student's question involves finding the typing speed in words per minute after 6 hours of practice, given several linear regression equations and their corresponding correlation coefficients (r). The best fitting model will provide the most accurate prediction for the typing speed after 6 hours. Among the options provided:

• Option a: The equation y = 4.9x + 17.1 with r = 0.971 predicts about 47 words per minute.
• Option d: The equation y = 5.1x + 17 with r = 0.971 also predicts about 47 words per minute.

Both options a and d have a high correlation coefficient of 0.971, suggesting a strong linear relationship between practice hours and typing speed. To determine which equation to use, we would typically choose the one with the higher r value, but since they are equal, we could base our decision on additional factors such as a plot of the data points or expert judgement. For this example, both options are equally likely without additional information.