Mathematical Statistics with Applications
7th Edition
ISBN: 9780495110811
Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer
Publisher: Cengage Learning
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Textbook Question
Chapter 11.4, Problem 16E
An experiment was conducted to observe the effect of an increase in temperature on the potency of an antibiotic. Three 1-ounce portions of the antibiotic were stored for equal lengths of time at each of the following Fahrenheit temperatures: 30◦, 50◦, 70◦, and 90◦. The potency readings observed at the end of the experimental period were as shown in the following table.
- a Find the least-squares line appropriate for this data.
- b Plot the points and graph the line as a check on your calculations.
- c Calculate S2.
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Read the following description of a data set.
Charles's landscape architecture firm won a contract to design a new public
playground in Seville. To decide how many swings to include, Charles collected
information about other playgrounds in the city.
For each playground, he recorded the area (in square metres), x, and the
number of swings, y.
The least squares regression line of this data set is:
y = 0.106x + 6.784
Complete the following sentence:
For each additional square metre of area, the least squares regression line predicts that a
playground would have
more swings.
Find the least-squares equation for the following pairs of data:
x = earthquake magnitude
2.9
4.2
3.3
4.5
2.6
3.2
3.4
y = depth of earthquake (in km)
5
10
11.2
10
7.9
3.9
5.5
A. y = 2.16 + 0.221x
B. y = 0.221 + 2.16x
C. y = 2.16 + 0.312x
D. y = 0.221 + 2.82x
Use the following information to answer questions 6 and 7.
In a study, nine tires of a particular brand were driven on a track under identical conditions. Each tire was driven a particular controlled distance (measured in thousands of miles) and the tread depth was measured after the drive. Tread depth is measured in
"mils." Here, 1 mil is 0.001 inch. The least-squares regression line was computed and added to a scatterplot of these data. On the plot, one data point is marked with an "X."
The equation of the least-squares regression line is:
Tread depth = 360.64 - 11.39 Miles
The data value marked with "X" in the provided scatterplot has
Tread Depth (Mils)
60
80
150
0
5
O a negative value for the residual.
O a positive value for the residual.
O a zero value for the residual.
O a zero value for the correlation.
10
15
Miles (x 1000)
20
25
30
Chapter 11 Solutions
Mathematical Statistics with Applications
Ch. 11.3 - If 0 and 1 are the least-squares estimates for the...Ch. 11.3 - Prob. 2ECh. 11.3 - Fit a straight line to the five data points in the...Ch. 11.3 - Auditors are often required to compare the audited...Ch. 11.3 - Prob. 5ECh. 11.3 - Applet Exercise Refer to Exercises 11.2 and 11.5....Ch. 11.3 - Prob. 7ECh. 11.3 - Laboratory experiments designed to measure LC50...Ch. 11.3 - Prob. 9ECh. 11.3 - Suppose that we have postulated the model...
Ch. 11.3 - Some data obtained by C.E. Marcellari on the...Ch. 11.3 - Processors usually preserve cucumbers by...Ch. 11.3 - J. H. Matis and T. E. Wehrly report the following...Ch. 11.4 - a Derive the following identity:...Ch. 11.4 - An experiment was conducted to observe the effect...Ch. 11.4 - Prob. 17ECh. 11.4 - Prob. 18ECh. 11.4 - A study was conducted to determine the effects of...Ch. 11.4 - Suppose that Y1, Y2,,Yn are independent normal...Ch. 11.4 - Under the assumptions of Exercise 11.20, find...Ch. 11.4 - Prob. 22ECh. 11.5 - Use the properties of the least-squares estimators...Ch. 11.5 - Do the data in Exercise 11.19 present sufficient...Ch. 11.5 - Use the properties of the least-squares estimators...Ch. 11.5 - Let Y1, Y2, . . . , Yn be as given in Exercise...Ch. 11.5 - Prob. 30ECh. 11.5 - Using a chemical procedure called differential...Ch. 11.5 - Prob. 32ECh. 11.5 - Prob. 33ECh. 11.5 - Prob. 34ECh. 11.6 - For the simple linear regression model Y = 0 + 1x...Ch. 11.6 - Prob. 36ECh. 11.6 - Using the model fit to the data of Exercise 11.8,...Ch. 11.6 - Refer to Exercise 11.3. Find a 90% confidence...Ch. 11.6 - Refer to Exercise 11.16. Find a 95% confidence...Ch. 11.6 - Refer to Exercise 11.14. Find a 90% confidence...Ch. 11.6 - Prob. 41ECh. 11.7 - Suppose that the model Y=0+1+ is fit to the n data...Ch. 11.7 - Prob. 43ECh. 11.7 - Prob. 44ECh. 11.7 - Prob. 45ECh. 11.7 - Refer to Exercise 11.16. Find a 95% prediction...Ch. 11.7 - Refer to Exercise 11.14. Find a 95% prediction...Ch. 11.8 - The accompanying table gives the peak power load...Ch. 11.8 - Prob. 49ECh. 11.8 - Prob. 50ECh. 11.8 - Prob. 51ECh. 11.8 - Prob. 52ECh. 11.8 - Prob. 54ECh. 11.8 - Prob. 55ECh. 11.8 - Prob. 57ECh. 11.8 - Prob. 58ECh. 11.8 - Prob. 59ECh. 11.8 - Prob. 60ECh. 11.9 - Refer to Example 11.10. Find a 90% prediction...Ch. 11.9 - Prob. 62ECh. 11.9 - Prob. 63ECh. 11.9 - Prob. 64ECh. 11.9 - Prob. 65ECh. 11.10 - Refer to Exercise 11.3. Fit the model suggested...Ch. 11.10 - Prob. 67ECh. 11.10 - Fit the quadratic model Y=0+1x+2x2+ to the data...Ch. 11.10 - The manufacturer of Lexus automobiles has steadily...Ch. 11.10 - a Calculate SSE and S2 for Exercise 11.4. Use the...Ch. 11.12 - Consider the general linear model...Ch. 11.12 - Prob. 72ECh. 11.12 - Prob. 73ECh. 11.12 - An experiment was conducted to investigate the...Ch. 11.12 - Prob. 75ECh. 11.12 - The results that follow were obtained from an...Ch. 11.13 - Prob. 77ECh. 11.13 - Prob. 78ECh. 11.13 - Prob. 79ECh. 11.14 - Prob. 80ECh. 11.14 - Prob. 81ECh. 11.14 - Prob. 82ECh. 11.14 - Prob. 83ECh. 11.14 - Prob. 84ECh. 11.14 - Prob. 85ECh. 11.14 - Prob. 86ECh. 11.14 - Prob. 87ECh. 11.14 - Prob. 88ECh. 11.14 - Refer to the three models given in Exercise 11.88....Ch. 11.14 - Prob. 90ECh. 11.14 - Prob. 91ECh. 11.14 - Prob. 92ECh. 11.14 - Prob. 93ECh. 11.14 - Prob. 94ECh. 11 - At temperatures approaching absolute zero (273C),...Ch. 11 - A study was conducted to determine whether a...Ch. 11 - Prob. 97SECh. 11 - Prob. 98SECh. 11 - Prob. 99SECh. 11 - Prob. 100SECh. 11 - Prob. 102SECh. 11 - Prob. 103SECh. 11 - An experiment was conducted to determine the...Ch. 11 - Prob. 105SECh. 11 - Prob. 106SECh. 11 - Prob. 107SE
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- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4arrow_forwardFind the mean hourly cost when the cell phone described above is used for 240 minutes.arrow_forwardc. Which of the following is the correct graph of the given data? -ОА. 10 1012 12 10 O C. 12- 81012 1012 Using the graph, explain the dramatic difference between the answers to parts (a) and (b). Choose the correct answer below. OA. The point (10,10) is not an outier, but it does have a strong effect on the least squares line and the correlation coefficient. OB. The point (10,10) does not have any effect on the least squares line and the correlation coefficient. OC. The point (10,10) is an outler that has a weak effect on the least squares line and the correlation coefficient. OD. The point (10,10) is an outlier that has a strong effect on the least squares line and the correlation coefficient.arrow_forward
- Read the following description of a data set. The owner of a bicycle store wonders if the employees who take the longest lunch breaks also make the fewest bicycle sales. One day, she notes the length of each salesperson's lunch break (in minutes), x, as well as the number of bicycles he or she sold that day, y. The least squares regression line of this data set is: ŷ = -0.297x + 10.889 Complete the following sentence: If a salesperson spends one additional minute at lunch, the least squares regression line predicts he or she will sell | fewer bicycles that day. Submit еarrow_forwardIn a statistics class, a teacher had the students complete an activity in which they grabbed as many bite-sized pretzels as they could with their dominant hand, without crushing them. The teacher then measured their handspan in centimeters. The scatterplot displays the data the teacher collected along with the least-squares regression line. One student with a handspan of 23 cm grabbed 38 pretzels. This point is circled on the graph. What effect will the circled point have on the y-intercept? The y-intercept will not change with the addition of this point. The y-intercept will decrease because the point pulls the least-squares regression line toward it. The y-intercept will increase because the point pulls the least-squares regression line toward it. The y-intercept will increase because this point represents an extremely high number of pretzels grabbed with the dominant hand.arrow_forwardA 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 (g) below. Click the icon to view the children's data. (a) Find the least-squares regression line treating height as the explanatory variable and head circumference as the response variable. y = .169 x+ ( 12.9) (Round the slope to three decimal places and round the constant to one decimal place as needed.) (b) Interpret the slope and y-intercept, if appropriate. First interpret the slope. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. For a height of 0 inches, the head circumference is predicted to be in. (Round to three decimal places as needed.) B. For a head circumference of 0 inches, the height is predicted to be in. (Round to three decimal places as…arrow_forward
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