Question

A typing instructor builds a regression model to investigate what factors determine typing speed for students with two months of instruction. Her regression equation looks like: Y' = 7x3 + 5x2 + 3x + 11 where: Y' = typing speed in words per minute; x3= hours of instruction per week; x2= hours of practice per week; x = hours of typing per week necessary for school or work; A new student is taking 2 hrs of typing instruction per week, will practice 5 hrs per week and must type 2.5 hours per week for work. If the standard error of the estimate is 4, within what range do we have a 95.45% probability that that student's typing speed will be in two months?A. 53.5 and 61.5 words per minuteB. 49.5 and 65.5 words per minuteC. 57.5 and 65.5 words per minuteD. none of the above

Answer 1

The range within which a student's typing speed will be in two months with a 95.45% probability is 49.66 to 65.34 words per minute.

Step-by-step explanation:

To find the range within which a student's typing speed will be in two months with a 95.45% probability, we need to calculate the prediction interval. The regression model equation is given as Y' = 7x3 + 5x2 + 3x + 11, where x3 represents hours of instruction per week, x2 represents hours of practice per week, and x represents hours of typing per week necessary for school or work.

Since the student is taking 2 hrs of typing instruction per week (x3 = 2), practicing 5 hrs per week (x2 = 5), and typing 2.5 hours per week for work (x = 2.5), we can substitute these values into the regression equation to find the predicted typing speed (Y').

Using the given equation and substituting the values, we get:

Y' = 7(2) + 5(5) + 3(2.5) + 11

Y' = 14 + 25 + 7.5 + 11 = 57.5 words per minute

Since the standard error of the estimate is 4, the prediction interval can be calculated by adding or subtracting 1.96 times the standard error from the predicted value. Therefore, the range for a 95.45% probability is:

57.5 - (1.96 x 4) to 57.5 + (1.96 x 4) = 57.5 - 7.84 to 57.5 + 7.84 = 49.66 to 65.34 words per minute.