Mathematical Statistics with Applications
7th Edition
ISBN: 9780495110811
Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 11.7, Problem 42E
Suppose that the model
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Heights (om) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 138 to 188 cm and weights of 41 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield
x 167.74 cm, y 81.46 ko, r0.239, Pvalue 0.017, and y - 106 + 1,15x. Find the best predicted value of y (weight) given an adult male who is 153 cm tall. Use a 0.01 significance level.
The best predicted value of y for an adult male who is 153 cm tall is kg.
(Round to two decimal places as needed.)
11) A simple linear regression model based on 20 observations. The F-stat for the model is 21.44 and the SSE is 1.41. The standard error for the coefficient of X is 0.2.
a) Complete the ANOVA table.
b) Find the t-stat of the co-efficient of X
c) Find the co-efficient of X.
Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 132 to 194 cm and weights of 38 to 150 kg. Let the
predictor variable x be the first variable given. The 100 paired measurements yield x 167.75 cm, y=81.58 kg, r0.318, P.value = 0.001, and y-109 1.14x.
Find the best predicted value of y (weight) given an adult male who is 184 cm tal, Use a 0.05 significance level.
The best predicted value of y for an adult male who is 184 cm tall is kg.
(Round to two decimal places as needed.)
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
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data are at or below for respiratory rates in breath per minute during the first 3 years of infancy are given by y=101.82411-0.0125995x+0.00013401x2 for awake infants and y=101.72858-0.0139928x+0.00017646x2 for sleeping infants, where x is the age in months. Source: Pediatrics. a. What is the domain for each function? b. For each respiratory rate, is the rate decreasing or increasing over the first 3 years of life? Hint: Is the graph of the quadratic in the exponent opening upward or downward? Where is the vertex? c. Verify your answer to part b using a graphing calculator. d. For a 1- year-old infant in the 95 th percentile, how much higher is the walking respiratory rate then the sleeping respiratory rate? e. f.arrow_forwardFind the equation of the regression line for the following data set. x 1 2 3 y 0 3 4arrow_forwardOlympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?arrow_forward
- A) A linear regression has a =6 and b=5 what is y predicted as when x=9? B) A linear regression has b=3 and a=4.What is the predicted Y for x=7?arrow_forwardHeights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 134 to 195 cm and weights of 38 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x- 167.55 cm, y 81.36 kg, r= 0.407, P-value = 0.000, and y = - 109 + 1.09x. Find the best predicted value of y (weight) given an adult male who is 140 cm tall. Use a 0.01 significance level. %3D The best predicted value of y for an adult male who is 140 cm tall is kg. (Round to two decimal places as needed.) Enter your answer in the answer box. MacBook Pro 吕0 O00 esc %23 24 % & delet 8. 6. 4. E T. Y. D F H. K Parrow_forwardThe sale of eggs that are contaminated with Salmonella can cause food poisoning among consumers. A large egg producer takes an SRS of 200 eggs from all the eggs shipped in one day. The laboratory reports that 11 of these eggs had Salmonella contamination. Unbeknownst to the producer, 0.2% of all eggs shipped had Salmonella. What is the best description of the values, 11 and 0.2%, in this situation? O 11 is a parameter and 0.2% is a statistic. O 0.2% is a parameter and 11 is a statistic. O Both 0.2% and 11 are parameters. Both 0.2% and 11 are statistics.arrow_forward
- The following data shows the atmospheric pollutants yi(relative to an EPA standard) at half hour interval xi. Find the equation y=a+bx of the least square line that best fits the data points given by 2,1, 5,2, 7,3, 8,3. Hence predict the atmospheric pollutant at x=6 half hour.arrow_forwardArm circumferences (cm) and heights (cm) are measured from randomly selected adult females. The 139 pairs of measurements yield x = 31.99 cm, y = 163.33 cm, r= 0.032, P-value = 0.708, and y = 158 + 0.1703x. Find the best predicted value of y (height) given an adult female with an arm circumference of 35.0 cm. Let the predictor variable x be arm circumference and the response variable y be height. Use a 0.05 significance level. %3D ..... The best predicted value is cm. (Round to two decimal places as needed.)arrow_forwardFind the least-squares regression line ŷ = ba + b₁ through the points (−2, 2), (3, 6), (5, 14), (8, 19), (10, 27), and then use it to find point estimates corresponding to x = 1 and x = = 7. For x = 1, y = For x = 7, y =arrow_forward
- Exercise 21. Assume that we have observed paired data 21,...,n and y₁,..., yn, and we want to describe these data using the model Y₁ = y + E, where e, are i.i.d. with E(₁) = 0. a) Using the least squares method, determine an estimator for the parameter 7. b) Show that your estimator is unbiased.arrow_forwardy y 90 54 50 53 80 91 35 41 60 48 35 61 60 71 40 56 60 71 55 68 40 47 65 36 55 53 35 11 50 68 60 70 65 57 90 79 50 79 35 59 A data set consist of dependent variable (y) and independent variable (x) as shown above. It is claims that the relationship between the x and y can be modelled through a regression model as follows: ŷ = a+bx where a and b are the estimated values for a and ß (refer to Appendix). (i) Determine the equation of the regression line to predict the y value from the x value. (ii) If the x value is 75, what is the value of y? (iii) Test the hypothesis that a=10 against the alternative a <10. Use a 0.05 level of significance. (iv) Construct a 95% prediction interval for the y with x=35.arrow_forward4. The following output from R presents the results from computing a linear model. In our data example we are interested to study the relationship between students' academic performance api00 with variable enroll which is the number of students in the school. Call: 1m (formula = api00 - enroll, data = d) Residuals: мin 10 Median 30 Маx -285.50 -112.55 -6.70 95.06 389.15 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 744.25141 enroll 15.93308 46.711 < 2e-16 *** -0.19987 0.02985 -6.695 7.34e-11 *** Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' 1 Residual standard error: 135 on 398 degrees of freedom Multiple R-squared: 0.1012, Adjusted R-squared: F-statistic: 44.83 on 1 and 398 DF, p-value: 7.339e-11 0.09898 a. Predict the monthly auto insurance premium for a driver with 10 years of driving experience. b. Compute the standard deviation of errors. c. Using alpha=0.05, test whether B, is different from zeroarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
Trigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,
College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Functions and Change: A Modeling Approach to Coll...
Algebra
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Cengage Learning
Trigonometry (MindTap Course List)
Trigonometry
ISBN:9781337278461
Author:Ron Larson
Publisher:Cengage Learning
Calculus For The Life Sciences
Calculus
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:Pearson Addison Wesley,
College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Statistics 4.1 Point Estimators; Author: Dr. Jack L. Jackson II;https://www.youtube.com/watch?v=2MrI0J8XCEE;License: Standard YouTube License, CC-BY
Statistics 101: Point Estimators; Author: Brandon Foltz;https://www.youtube.com/watch?v=4v41z3HwLaM;License: Standard YouTube License, CC-BY
Central limit theorem; Author: 365 Data Science;https://www.youtube.com/watch?v=b5xQmk9veZ4;License: Standard YouTube License, CC-BY
Point Estimate Definition & Example; Author: Prof. Essa;https://www.youtube.com/watch?v=OTVwtvQmSn0;License: Standard Youtube License
Point Estimation; Author: Vamsidhar Ambatipudi;https://www.youtube.com/watch?v=flqhlM2bZWc;License: Standard Youtube License