Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 12.2, Problem 27E
To determine
Derive the least squares estimate of
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Find 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 =
Consider the points (1, 1), (2, 3), (−3, 1). Find the least squares regression line.
Find the least-squares regression line ŷ =b0+b1x through the points
(-2,2), (2,6), (5,13),(8,20),(10,24).
For what value of x is ŷ =0?
x =?
Chapter 12 Solutions
Probability and Statistics for Engineering and the Sciences
Ch. 12.1 - The efficiency ratio for a steel specimen immersed...Ch. 12.1 - The article Exhaust Emissions from Four-Stroke...Ch. 12.1 - Bivariate data often arises from the use of two...Ch. 12.1 - The accompanying data on y = ammonium...Ch. 12.1 - The article Objective Measurement of the...Ch. 12.1 - One factor in the development of tennis elbow, a...Ch. 12.1 - The article Some Field Experience in the Use of an...Ch. 12.1 - Referring to Exercise 7, suppose that the standard...Ch. 12.1 - The flow rate y (m3/min) in a device used for...Ch. 12.1 - Suppose the expected cost of a production run is...
Ch. 12.1 - Suppose that in a certain chemical process the...Ch. 12.2 - Refer back to the data in Exercise 4, in which y =...Ch. 12.2 - The accompanying data on y = ammonium...Ch. 12.2 - Refer to the lank temperature-efficiency ratio...Ch. 12.2 - Values of modulus of elasticity (MOE, the ratio of...Ch. 12.2 - The article Characterization of Highway Runoff in...Ch. 12.2 - For the past decade, rubber powder has been used...Ch. 12.2 - For the past decade, rubber powder has been used...Ch. 12.2 - The following data is representative of that...Ch. 12.2 - The bond behavior of reinforcing bars is an...Ch. 12.2 - Wrinkle recovery angle and tensile strength are...Ch. 12.2 - Calcium phosphate cement is gaining increasing...Ch. 12.2 - a. Obtain SSE for the data in Exercise 19 from the...Ch. 12.2 - The invasive diatom species Didymosphenia geminata...Ch. 12.2 - Prob. 25ECh. 12.2 - Show that the point of averages (x,y) lies on the...Ch. 12.2 - Prob. 27ECh. 12.2 - a. Consider the data in Exercise 20. Suppose that...Ch. 12.2 - Consider the following three data sets, in which...Ch. 12.3 - Reconsider the situation described in Exercise 7,...Ch. 12.3 - During oil drilling operations, components of the...Ch. 12.3 - Exercise 16 of Section 12.2 gave data on x =...Ch. 12.3 - During oil drilling operations, components of the...Ch. 12.3 - For the past decade, rubber powder has been used...Ch. 12.3 - Refer back to the data in Exercise 4, in which y =...Ch. 12.3 - Misi (airborne droplets or aerosols) is generated...Ch. 12.3 - Prob. 37ECh. 12.3 - Refer to the data on x = liberation rate and y =...Ch. 12.3 - Carry out the model utility test using the ANOVA...Ch. 12.3 - Prob. 40ECh. 12.3 - Prob. 41ECh. 12.3 - Verify that if each xi is multiplied by a positive...Ch. 12.3 - Prob. 43ECh. 12.4 - Fitting the simple linear regression model to the...Ch. 12.4 - Reconsider the filtration ratemoisture content...Ch. 12.4 - Astringency is the quality in a wine that makes...Ch. 12.4 - The simple linear regression model provides a very...Ch. 12.4 - Prob. 48ECh. 12.4 - You are told that a 95% CI for expected lead...Ch. 12.4 - Prob. 50ECh. 12.4 - Refer to Example 12.12 in which x = test track...Ch. 12.4 - Plasma etching is essential to the fine-line...Ch. 12.4 - Consider the following four intervals based on the...Ch. 12.4 - The height of a patient is useful for a variety of...Ch. 12.4 - Prob. 55ECh. 12.4 - The article Bone Density and Insertion Torque as...Ch. 12.5 - The article Behavioural Effects of Mobile...Ch. 12.5 - The Turbine Oil Oxidation Test (TOST) and the...Ch. 12.5 - Toughness and fibrousness of asparagus are major...Ch. 12.5 - Head movement evaluations are important because...Ch. 12.5 - Prob. 61ECh. 12.5 - Prob. 62ECh. 12.5 - Prob. 63ECh. 12.5 - The accompanying data on x = UV transparency index...Ch. 12.5 - Torsion during hip external rotation and extension...Ch. 12.5 - Prob. 66ECh. 12.5 - Prob. 67ECh. 12 - The appraisal of a warehouse can appear...Ch. 12 - Prob. 69SECh. 12 - Forensic scientists are often interested in making...Ch. 12 - Phenolic compounds are found in the effluents of...Ch. 12 - The SAS output at the bottom of this page is based...Ch. 12 - The presence of hard alloy carbides in high...Ch. 12 - The accompanying data was read from a scatterplot...Ch. 12 - An investigation was carried out to study the...Ch. 12 - Prob. 76SECh. 12 - Open water oil spills can wreak terrible...Ch. 12 - In Section 12.4, we presented a formula for...Ch. 12 - Show that SSE=Syy1Sxy, which gives an alternative...Ch. 12 - Suppose that x and y are positive variables and...Ch. 12 - Let sx and sy denote the sample standard...Ch. 12 - Verify that the t statistic for testing H0: 1 = 0...Ch. 12 - Use the formula for computing SSE to verify that...Ch. 12 - In biofiltration of wastewater, air discharged...Ch. 12 - Normal hatchery processes in aquaculture...Ch. 12 - Prob. 86SECh. 12 - Prob. 87SE
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
- Olympic 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_forwardAn experiment was performed on a certain metal to determine if the strength is a function of heating time. Results based on 10 metal sheets are given below. ∑ X = 30 ∑ X 2 = 104 ∑ Y = 40 ∑ Y 2 = 178 ∑ XY = 134 Using the simple linear regression model, find the estimated y-intercept and slope and write the equation of the least squares regression line.arrow_forwardAn owner of a home in the Midwest installed solar panels to reduce heating costs. After installing the solar panels, he measured the amount of natural gas use y (in cubic feet) to heat the home and outside temperature x (in degree-days, where a day’s degree-days are the number of degrees its average temperature falls below 65F) over a 23-month period. He then computed the least squares regression line for predicting y from x and found it to be, ŷ=85+16x How much, on average, does gas used increase for each additional degree-day? The predicted amount of gas used when the outside temperature is 20 degree- days.arrow_forward
- y 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_forwardUse the general equation for the least square regression line to show that this line always passes through the point (x,y) * bars above the x and y.That is, set x=x(with a bar above the x) and show that the line predicts that y=y (with a bar above the y).arrow_forwardAn owner of a home in the Midwest installed solar panels to reduce heating costs. After installing the solar panels, he measured the amount of natural gas used y (in cubic feet) to heat the home and outside temperature x (in degree-days, where a day's degree-days are the number of degrees its average temperature falls below 65° F) over a 23-month period. He then computed the least-squares regression line for predicting y from x and found it to be ŷ = 85 + 16x. The software used to compute the least-squares regression line for the equation above says that r2 = 0.98. This suggests which of the following? 1. Gas used increases by square root of 0.98 = 0.99 cubic feet for each additional degree-day? 2. Although degree-days and gas used are correlated, degree-days do not predict gas used very accurately. 3. Prediction of gas used from degree-days will be quite accurate.arrow_forward
- Find the equation y = Bo + B,x of the least-squares line that best fits the given data points. %3D (-1,0), (0,2), (1,4), (2,7) The line is y =D+ Ox. (Type integers or decimals.)arrow_forwardFind the least-squares regression line âŷ = bo + br through the points (-2,0), (3, 9), (5, 13), (7, 18), (12, 24). For what value of z is y = 0? I =arrow_forwardFind the least-squares regression line ŷ = bo + b1r through the points %3D (-1,2), (2, 6), (5, 13), (7, 20), (10, 23), and then use it to find point estimates y corresponding to x = 3 and x = 6. For = 3, y = %3D For I = 6, y = %3Darrow_forward
- The least squares regression line for a set of data is calculated to be y = 24.8 + 3.41x. (a) One of the points in the data set is (4, 37). Calculate the predicted value. (b) For the point in part (a), calculate the residual.arrow_forwardFind the least squares regression line for the points (−3, 0), (−1, 1), (0, 2), and (2, 3).arrow_forwardThe relationship between number of beers consumed (x) and blood alcohol content (y) was studied in 16 male college students by using least squares regression. The following regression equation was obtained from this study: y-hat = -0.0127 + 0.0180x The above equation implies that: each beer consumed increases blood alcohol by .0127 on average it takes 1.8 beers to increase blood alcohol content by .01 After consuming 1 beer, blood alcohol equals .0180. each beer consumed increases blood alcohol by 0.018arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage LearningCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:9781305658004
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,
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Correlation Vs Regression: Difference Between them with definition & Comparison Chart; Author: Key Differences;https://www.youtube.com/watch?v=Ou2QGSJVd0U;License: Standard YouTube License, CC-BY
Correlation and Regression: Concepts with Illustrative examples; Author: LEARN & APPLY : Lean and Six Sigma;https://www.youtube.com/watch?v=xTpHD5WLuoA;License: Standard YouTube License, CC-BY