Essential Statistics
2nd Edition
ISBN: 9781259570643
Author: Navidi
Publisher: MCG
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 11, Problem 7RE
a.
To determine
Find the least-square regression line for predicting drying time (y) using concentration (x).
b.
To determine
Construct the 95% confidence interval for the slope coefficient.
c.
To determine
Test the significance of concentration in predicting the drying time at 5% level of significance.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Computer output from a least-squares regression analysis based on a sample of size 17 is shown in the table.
Term
COEFCOEF
SE CoefSE Coef
TT
Constant
7.43
0.59
12.59
xx
5.65
1.14
6.45
Assuming all conditions for inference are met, which of the following defines a 95 percent confidence interval for the slope of the least-squares regression line?
A linear regression model was fit to a set of data containing 18 observations. The computer output of the regression analysis is shown in the table.
Term
CoefCoef
SE CoefSE Coef
TT
Constant
12.00
5.43
2.210
xx
0.694
0.241
2.880
Assume the conditions for regression are met. Which of the following defines the margin of error when a 95 percent confidence interval for the slope of the least-squares regression line is calculated?
(1.75)(0.241)
A
(1.75)(0.694)
B
(1.96)(0.241)
C
(2.12)(0.241))
D
(2.12)(0.694)
E
A psychological study aimed at predicting Al Ain secondary school students’ mental health scores via their scores in the life satisfaction scale. The researcher examines the following null hypothesis: there is no significant relationship between Al Ain secondary school students’ mental health and their life satisfaction scores at 0.05 level of significance.
Use the following data to establish the required regression equation.
Student #
Mental health score out of 50
Life- satisfaction score out of 100
1
40
80
2
41
87
3
34
90
4
30
78
5
44
89
6
42
85
7
45
88
8
32
77
9
47
90
10
22
57
11
30
78
12
28
77
13
35
76
14
40
84
15
31
76
16
39
80
17
41
84
18
24
60
19
22
50
20
37
75
21
40
80
22
38
78
23
29
60
24
24
55
25
24
62
26
29
61
27
32
65
28
34
66
29
28
67…
Chapter 11 Solutions
Essential Statistics
Ch. 11.1 - Prob. 1CYUCh. 11.1 - Prob. 2CYUCh. 11.1 - Prob. 3CYUCh. 11.1 - Prob. 4CYUCh. 11.1 - Prob. 5CYUCh. 11.1 - Prob. 6CYUCh. 11.1 - Prob. 7CYUCh. 11.1 - Prob. 8CYUCh. 11.1 - Prob. 9ECh. 11.1 - Prob. 10E
Ch. 11.1 - Prob. 11ECh. 11.1 - Prob. 12ECh. 11.1 - Prob. 13ECh. 11.1 - Prob. 14ECh. 11.1 - Prob. 15ECh. 11.1 - Prob. 16ECh. 11.1 - Prob. 17ECh. 11.1 - Prob. 18ECh. 11.1 - Prob. 19ECh. 11.1 - Prob. 20ECh. 11.1 - Prob. 21ECh. 11.1 - Prob. 22ECh. 11.1 - Prob. 23ECh. 11.1 - Prob. 24ECh. 11.1 - Prob. 25ECh. 11.1 - Prob. 26ECh. 11.1 - Prob. 27ECh. 11.1 - In Exercises 25–30, determine whether the...Ch. 11.1 - Prob. 29ECh. 11.1 - Prob. 30ECh. 11.1 - Prob. 31ECh. 11.1 - Prob. 32ECh. 11.1 - 33. Pass the ball: The NFL Scouting Combine is an...Ch. 11.1 - 34. Carbon footprint: Carbon dioxide (CO2) is...Ch. 11.1 - 35. Foot temperatures: Foot ulcers are a common...Ch. 11.1 - Prob. 36ECh. 11.1 - Prob. 37ECh. 11.1 - Prob. 38ECh. 11.1 - Prob. 39ECh. 11.1 - Prob. 40ECh. 11.1 - Prob. 41ECh. 11.1 - Prob. 42ECh. 11.1 - Prob. 43ECh. 11.2 - 1. The following table presents the percentage of...Ch. 11.2 - 2. At the final exam in a statistics class, the...Ch. 11.2 - 3. For each of the following plots, interpret the...Ch. 11.2 - Prob. 4CYUCh. 11.2 - Prob. 5ECh. 11.2 - In Exercises 5–7, fill in each blank with the...Ch. 11.2 - Prob. 7ECh. 11.2 - Prob. 8ECh. 11.2 - In Exercises 8–12, determine whether the statement...Ch. 11.2 - Prob. 10ECh. 11.2 - Prob. 11ECh. 11.2 - Prob. 12ECh. 11.2 - Prob. 13ECh. 11.2 - Prob. 14ECh. 11.2 - Prob. 15ECh. 11.2 - Prob. 16ECh. 11.2 - Prob. 17ECh. 11.2 - Prob. 18ECh. 11.2 - Prob. 19ECh. 11.2 - Prob. 20ECh. 11.2 - Prob. 21ECh. 11.2 - Prob. 22ECh. 11.2 - Prob. 23ECh. 11.2 - Prob. 24ECh. 11.2 - Prob. 25ECh. 11.2 - Prob. 26ECh. 11.2 - 27. Blood pressure: A blood pressure measurement...Ch. 11.2 - Prob. 28ECh. 11.2 - 29. Interpreting technology: The following display...Ch. 11.2 - Prob. 30ECh. 11.2 - Prob. 31ECh. 11.2 - Prob. 32ECh. 11.2 - Prob. 33ECh. 11.2 - Prob. 34ECh. 11.2 - Prob. 35ECh. 11.3 - Prob. 1CYUCh. 11.3 - Prob. 2CYUCh. 11.3 - Prob. 3CYUCh. 11.3 - Prob. 4CYUCh. 11.3 - Prob. 5CYUCh. 11.3 - Prob. 6CYUCh. 11.3 - Prob. 7ECh. 11.3 - Prob. 8ECh. 11.3 - Prob. 9ECh. 11.3 - Prob. 10ECh. 11.3 - Prob. 11ECh. 11.3 - Prob. 12ECh. 11.3 - Prob. 13ECh. 11.3 - Prob. 14ECh. 11.3 - Prob. 15ECh. 11.3 - Prob. 16ECh. 11.3 - Prob. 17ECh. 11.3 - Prob. 18ECh. 11.3 - Calories and protein: The following table presents...Ch. 11.3 - Prob. 20ECh. 11.3 - Butterfly wings: Do larger butterflies live...Ch. 11.3 - Blood pressure: A blood pressure measurement...Ch. 11.3 - Prob. 23ECh. 11.3 - Prob. 24ECh. 11.3 - Getting bigger: Concrete expands both horizontally...Ch. 11.3 - Prob. 26ECh. 11.3 - Prob. 27ECh. 11.3 - Prob. 28ECh. 11.3 - Prob. 29ECh. 11.3 - Prob. 30ECh. 11.3 - Prob. 31ECh. 11.4 - Prob. 1CYUCh. 11.4 - Prob. 2CYUCh. 11.4 - Prob. 3ECh. 11.4 - Prob. 4ECh. 11.4 - Prob. 5ECh. 11.4 - Prob. 6ECh. 11.4 - Prob. 7ECh. 11.4 - Prob. 8ECh. 11.4 - Prob. 9ECh. 11.4 - Prob. 10ECh. 11.4 - Calories and protein: Use the data in Exercise 19...Ch. 11.4 - Prob. 12ECh. 11.4 - Butterfly wings: Use the data in Exercise 21 in...Ch. 11.4 - Prob. 14ECh. 11.4 - Prob. 15ECh. 11.4 - Prob. 16ECh. 11.4 - Prob. 17ECh. 11.4 - Prob. 18ECh. 11.4 - Prob. 19ECh. 11.4 - Prob. 20ECh. 11.4 - Prob. 21ECh. 11 - Prob. 1CQCh. 11 - Prob. 2CQCh. 11 - Prob. 3CQCh. 11 - Prob. 4CQCh. 11 - Prob. 5CQCh. 11 - Prob. 6CQCh. 11 - Prob. 7CQCh. 11 - Prob. 8CQCh. 11 - Prob. 9CQCh. 11 - Prob. 10CQCh. 11 - Prob. 11CQCh. 11 - Prob. 12CQCh. 11 - Prob. 13CQCh. 11 - Prob. 14CQCh. 11 - Prob. 15CQCh. 11 - Prob. 1RECh. 11 - Prob. 2RECh. 11 - Prob. 3RECh. 11 - Prob. 4RECh. 11 - Prob. 5RECh. 11 - Prob. 6RECh. 11 - Prob. 7RECh. 11 - Prob. 8RECh. 11 - Prob. 9RECh. 11 - Prob. 10RECh. 11 - Prob. 11RECh. 11 - Prob. 12RECh. 11 - Prob. 13RECh. 11 - Interpret technology: The following TI-84 Plus...Ch. 11 - Prob. 15RECh. 11 - Prob. 1WAICh. 11 - Prob. 2WAICh. 11 - Prob. 3WAICh. 11 - Prob. 4WAICh. 11 - Prob. 5WAICh. 11 - Prob. 6WAICh. 11 - Prob. 7WAICh. 11 - Prob. 1CSCh. 11 - Prob. 2CSCh. 11 - Prob. 3CSCh. 11 - Prob. 4CSCh. 11 - Prob. 5CSCh. 11 - Prob. 6CSCh. 11 - Prob. 7CSCh. 11 - Prob. 8CSCh. 11 - Prob. 9CSCh. 11 - Prob. 10CSCh. 11 - Prob. 11CS
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
- Now, the predictors flyer and display were added to the dataset and a multiple linear regression model was fitted. Part of the R output is shown below – Estimate Standard Error Intercept 81.23 35.24 Price -0.0318 0.023 Flyer 10.21 3.28 Display 21.67 13.27 Adj R Square = 78.8% Calculate a 95% confidence interval of Flyer and interpret the same in the context of the problem. Can we say that promoting a product through fliers significantly affect its sales? What is the coefficient of multiple determination of this model? Interpret its value.arrow_forwardConsider the regression model Y = B0 + B1 X1 + B2 X2 + u. Suppose you want to test the null hypothesis H0: B1 + B2 = 0, versus the alternative hypothesis H1: B1+ B2 != 0 (!= means "not equal to"). The data set consists of 100 observations. (a) Suppose we use an F-statistic to conduct the test. What are the degrees of freedom associated with this test statistic? (b) Let G(.) be the CDF of the F-distribution for the F-statistic in part (b). Denote the actual F-statistic by F_act. Suppose someone says that you should reject the null at the 5% significance level if G(F_act)<0.05. Explain whether you agree with this approach. (c) Suppose you find that the F-test in part (b)-(c) and the test in part (a) yield very different p-values. Do you think this result is correct? Briefly explain your reasoning.arrow_forwardIn a simple regression analysis for a given data set, if the null hypothesis β = 0 is rejected, then the null hypothesis ρ = 0 is also rejected. This statement is ___________ true.arrow_forward
- The height (in feet) and trunk circumference (in inches) at breast height (4.5 feet above the ground)was measured for a random sample of Eucalyptus trees. The data are summarized below.Trunk Circumference 21.1 20.8 22.5 19.4 23.6 19.8 21.6 19.9Tree Height 34.2 32.7 35.0 31.9 36.5 31.2 33.8 31.4(a) Determine the linear regression model that will best predict the height of a Eucalyptus treebased on its trunk circumference at breast height.arrow_forwardIn a simple linear regression model with one predictor variable, what is the coefficient of determination (R-squared) if the Pearson's correlation coefficient between the predictor and response variable is 0.6?arrow_forwardA study of emergency service facilities investigated the relationship between the number of facilities and the average distance traveled to provide the emergency service. The following table gives the data collected. Number ofFacilities AverageDistance(miles) 9 1.66 11 1.13 16 0.83 21 0.61 27 0.51 30 0.46 2. .Does a simple linear regression model appear to be appropriate? Explain. a.No, the scatter diagram suggests that there is no relationship. b.No, the scatter diagram suggests that there is a curvilinear relationship. c.Yes, the scatter diagram suggests that there is a linear relationship. 3.Develop an estimated regression equation for the data corresponding to a second-order model with one predictor variable. (Round your numerical values to four decimal places.)arrow_forward
- a) Calculate the least square regression line for X on Y of the given data?b) Calculate the coefficient of correlation of the given date? Interpret the value of the coefficient?arrow_forwardGiven the estimated least square regression line y=2.48+1.63x, and the coefficient of determination of 0.81, What is the value of correlation coefficient?arrow_forwardIf there is no significant correlation between the response and explanatory variables, would the slope of the regression line be (a) positive (b) negative (c) zero?arrow_forward
- A newspaper used an estimated regression equation to describe the relationship between y = error percentage for subjects reading a four-digit liquid crystal display and the independent variables x1 = level of backlight, x2 = character subtense, x3 = viewing angle, and x4 = level of ambient light. From a table given in the article, SSRegr = 21.6, SSResid = 22, and n = 30. What is the value of the test statistic F What is the P-value What is r2 What is Searrow_forwardWHat is the confidence interval? Consider the following data on x = rainfall volume (m3) and y = runoff volume (m3) for a particular location. x 5 12 14 18 23 30 40 46 55 67 72 83 96 112 127 y 4 10 13 14 15 25 27 45 38 46 53 71 82 99 105 Use the accompanying Minitab output to decide whether there is a useful linear relationship between rainfall and runoff. The regression equation isrunoff = -2.05 + 0.847 rainfall Predictor Coef Stdev t-ratio p Constant -2.049 2.251 -0.91 0.379 rainfall 0.84717 0.03465 24.45 0.000 s = 4.978 R-sq = 97.9% R-sq(adj) = 97.7% State the appropriate null and alternative hypotheses. H0: β1 = 0 Ha: β1 ≠ 0 H0: β1 ≠ 0 Ha: β1 = 0 H0: β1 = 0 Ha: β1 < 0 H0: β1 = 0 Ha: β1 > 0 Compute the test statistic value and find the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) t = P-value = State the conclusion in the problem context. (Use α = 0.05.) Reject H0. There…arrow_forwardBased on the following output tables, write all the panel data regression models. Which is a better model, FEM or REM? Justify your answer. Table A: Dependent Variable: PAYOUT_RATIO Method: Panel Least Squares Variable Coefficient Std. Error t-Statistic Prob. FOREIGN_DIRECTORS 158.8968 14.70223 10.80766 0.0000 FEMALE_DIRECTORS -4.463537 36.09961 -0.123645 0.9023 C 3.143324 5.364327 0.585968 0.5618 Effects Specification Cross-section fixed (dummy variables) R-squared 0.876583 Mean dependent var 38.31686 Adjusted R-squared 0.840284 S.D. dependent var 59.89422 S.E. of regression 23.93641 Akaike info criterion 9.397265 Sum squared…arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman
MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning
Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman
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