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
Textbook Question
Chapter 11.10, Problem 66E
Refer to Exercise 11.3. Fit the model suggested there by use of matrices.
11.3 Fit a straight line to the five data points in the accompanying table. Give the estimates of β0 and β1. Plot the points and sketch the fitted line as a check on the calculations.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
The table below shows the number of state-registered automatic weapons and the murder rate for several
Northwestern states.
X 11.3
y
13.3 10.9 9.9
8.4 6.8 3.9
2.8 2.4 2.5
7 6.7 6.4 6.3
x = thousands of automatic weapons
y = murders per 100,000 residents
This data can be modeled by the equation ŷ = 0.79x + 4.32. Use this equation to answer the following.
Answer = 12.829
0.9
5
A) How many murders per 100,000 residents can be expected in a state with 10.1 thousand automatic
weapons?
Answer = 6.123
x Round to 3 decimal places.
B) How many murders per 100,000 residents can be expected in a state with 2.7 thousand automatic
weapons?
x Round to 3 decimal places.
Find the best approximation to a = (3,-7, 2, 3)
= (2,-1.-3, 1) and = (1, 1,0,-1).
as a linear combination of
%3D
4.
Refer to the data set: (1, 2.5), (2.5, 15), (0.5, 2), (-2, 0.5), (0, 1), (1.5, 5)Part a: Make a scatterplot and determine which type of model best fits the data.Part b: Find the regression equation, round decimals to one place.Part c: Use the equation from Part b to determine y when x = 6.
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
- Does Table 1 represent a linear function? If so, finda linear equation that models the data.arrow_forwardThe table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. 11.6 8.6 6.9 3.9| 2.4 2.2 2.6 0.6 14 11.2 10 7.5 6.1 6 6.3 4.3 x = thousands of automatic weapons y = murders per 100,000 residents This data can be modeled by the equation y = 0.86x + 4.01. Use this equation to answer the following; A) How many murders per 100,000 residents can be expected in a state with 1.4 thousand automatic weapons? Answer = Round to 3 decimal places. B) How many murders per 100,000 residents can be expected in a state with 5.1 thousand automatic weapons? Answer = Round to 3 decimal places.arrow_forwardThe table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. 11.5 8.4 6.8 3.4 2.5 2.6 2.6 0.9 13.5 10.9 9.8 6.7 6.3 6.4 4.5 x = thousands of automatic weapons y = murders per 100,000 residents This data can be modeled by the equation 0.83x + 3.99. Use this equation to answer the following; Special Note: I suggest you verify this equation by performing linear regression on your calculator. A) How many murders per 100,000 residents can be expected in a state with 8.4 thousand automatic weapons? Answer Round to 3 decimal places. B) How many murders per 100,000 residents can be expected in a state with 7.3 thousand automatic weapons? Answer Round to 3 decimal places.arrow_forward
- The data show the number of felony convictions, in hundreds, and the crime rate, in crimes per 100,000, for seven randomly selected states. For the given data, a. determine the correlation coefficient between the number of felony convictions and the crime rate, (b) find the equation of the regression line, (c) approximate what crime rate can we anticipate in a state that has 12 hundred felony convictions.Felony convictions: 11.4, 8.1, 6.7, 3.4, 2.4, 2.3, 0.4Crime rate/ 100,000: 12, 9.5, 10.4, 9, 4.2, 5.5, 3.3 A. a. r = 0.906 b. y = 3.85x + 0.777 c. 47 B. a. r = 0.906 b. y = 0.777x + 3.85 c. 13.2 C. a. r = -0.906 b. y = 0.777x - 3.85 c. 5.5 D. a. r = -0.906 b. y = -0.777x + 3.85 c. 5.5arrow_forwardRefer to the data set: Part a: Make a scatterplot and determine which type of model best fits the data.Part b: Find the regression equation, round to two decimal places if necessary.Part c: Use the equation from Part b to determine y when x = -3.6.arrow_forwardThe table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. 11.6 8.1 7.1 3.9 2.9 2.6 2.1 0.7 13.7 10.7 10.2 7 6.5 6.5 5.7 4.7 thousands of automatic weapons y = murders per 100,000 residents This data can be modeled by the linear equation 0.83x + 4.08 a. How many murders per 100,000 residents can be expected in a state with 10.3 thousand automatic weapons? Round to 3 decimal places. murders per 100,000 residents b. How many murders per 100,000 residents can be expected in a state with 2.5 thousand automatic weapons? Round to 3 decimal places. murders per 100,000 residentsarrow_forward
- The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. 11.5 7. 11.2 8.5 3.7 2.4 2.7 2.1 0.4 13.6 10 7.5 6. 6.2 5.5 4.1 I = thousands of automatic weapons y= murders per 100,000 residents This data can be modeled by the linear equation ý = 0.86x +3.92 a. How many murders per 100,000 residents can be expected in a state with 2.2 thousand automatic weapons? Round to 3 decimal places. murders per 100,000 residents b. How many murders per 100,000 residents can be expected in a state with 6 thousand automatic weapons? Round to 3 decimal places. murders per 100,000 residents Question Help: Video Submit Questionarrow_forwardPlease give handwrittenarrow_forwardRefer to the data set:(-1, 2), (1, 3), (1, 5), (2, 7), (3, 8), (4, 11)Part a: Make a scatter plot and determine which type of model best fits the data.Part b: Find the regression equation.Part c: Use the equation from Part b to determine y when x = 10arrow_forward
- I need help making a equation that would work for my table/data.arrow_forwardSeveral neurosurgeons want to determine whether a dynamic system reduced the number of acute postoperative days in the hospital relative to a static system. The table shows data the neurosurgeons collected. Complete parts (a) and (b) below. Click the icon to view the data table. a. Obtain dotplots for each of the two data sets, using the same scales. Choose the correct dotplot below. O A. 6 8 10 12 14 16 18 Acute Postoperative Days O B. il 46 8 10 12 14 16 18 Acute Postoperative Days b. Use the result from part (a) to compare the two data sets. OA. The number of acute postoperative days is, on average, less with the static system than with the dynamic system. However, the static system produces more variation in the number of days. B. The number of acute postoperative days is, on average, less with the static system than with the dynamic system. Also, the dynamic system produces more variation in the number of days. O C. The number of acute postoperative days is, on average, less with…arrow_forwardGiven the data (1,2), (3,6) and (5,14). Use the method of least squares to calculate the estimated regression. coefficients.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
- Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Matrix Operations Full Length; Author: ProfRobBob;https://www.youtube.com/watch?v=K5BLNZw7UeU;License: Standard YouTube License, CC-BY
Intro to Matrices; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=yRwQ7A6jVLk;License: Standard YouTube License, CC-BY