4.2 Statistics
20. Suppose the line y = 2.8333x - 22.4967 describes the relation between the clubhead speed (in miles per hour). x and the distance a golf ball travels (in y- (a) Predict the distance a golf ball will travel if the club-head speed is 100 mph. (b) Suppose the observed distance a golf ball traveled when the club-head speed was 100 mph was 265 yards. What is the residual? a The olf ball will travel ards. 9 y (Round to the nearest tenth as needed.) (b) The residual is . (Round to the nearest tenth as needed.) 21. A pediatrician wants to determine the relation that exists between a child's height, x, and head circumference, y. She randomly selects 11 children from her practice, measures their heights and head circumferences and obtains the accompanying data. Complete parts (a) through (e). 4 Click the icon to view the data table. (it) Find the leastsquares regression line treating height as the explanatory variable and head circumference as the response variable. The leastsquares regression line is = I x + I (Round to four decimal places as needed.) (b) Use the regression equation to predict the head circumference of a child who is 25 inches tall. The predicted value of the head circumference of a child who is 25 inches tail is inches. (Round to two decimal places as needed.) (6) Compute the residual based on the observed head circumference of the 25inchtall child in the table. Is the head circumference of this child above average or below average? The residual based on the observed head circumference of the 25inchtall child is ):| inches. (Round to two decimal places as needed.) (d) Draw the least-squares regression line on the scatter diagram of the data and label the residual from part (c). Choose the correct graph below. OA. 05. 0c. 3 I I I I I 9.9 17, e a Hem c'rmmtarmca (In) Head crwmference an) :2 Head crmmbme (m) s W , t !-> 24 26 28 24 25 25 26 Hctght (in) Helgnt (in) Hctgtlt (in) Is the head circumference of this child above average or below average? O Above average 0 Below average (9) Notice that two children are 26.75 inches tall. One has a head circumference of 17.3 inches; the other has a head circumference of 17.5 inches. How can this be? 0 A. For children who are 26.75 inches tall, head circumference varies. O B. It is a mistake among the measurements. O C. It is not appropriate to use this model to predict the value of the head circumference for children who are 26.75 inches tall because 26.75 inches is outside the scope of the model. 4: Data Table Fulidata set 91 Height, Head circumference, Height, Heed circumference, x (inches) y ("mm\") x (inches) y (Inches) 27.75 17.5 27 17.3 24.5 17.1 27.5 17.5 25.5 17.1 26.75 17.3 25.5 17.3 26.75 17.5 25 16.9 27.5 17.5 27.75 17.5 22. The data below represent the number of days absent. x. and the nal grade. y. for a sample of college students at a large university. Complete parts (a) through (e) below. No.ofabsances,x U 'l 2 3 4 5 6 7 a 9 @ Finalgrade,y 88.9 66.0 83.0 80.6 77.6 73.2 63.9 68.1 65.2 62.3 (:1) Find the leastsquares regression line treating the number of absences, x, as the explanatory variable and the nal grade, y, as the response variable. A v = l:|x + (:1 (Round to three decimal places as needed.) (b) Interpret the slope and y-intercept, if appropriate. Interpret the slope. Select the correct choice below and. if necessary. fill in the answer box to complete your choice. (Round to three decimal places as needed.) 0 A- For every unit change in the nal grade, the number of days absent falls by days, on average. 0 5- For zero days absent. the nal score is predicted to be . O C. For a final score of zero, the number of days absent is predicted to be days. 0 D. For every day absent. the nal grade falls by , on average. 0 E. It is not appropriate to interpret the slope. Interpret the yintercept. Select the correct choice below and. if necessary. ll in the answer box to complete your choice. (Round to three decimal places as needed.) 0 A. For every unit change in the nal grade, the number of days absent falls by days, on average. 0 5- For zero days absent. the nal score is predicted to be . O C. For a final score of zero, the number of days absent is predicted to be days. 0 D. For every day absent. the nal grade falls by , on average. 0 E. It is not appropriate to interpret the y-intercept. (c) Predict the nal grade for a student who misses five class periods and compute the residual. Is the observed nal grade above or below average for this number of absences
