Understanding Basic Statistics
8th Edition
ISBN: 9781337558075
Author: Charles Henry Brase, Corrinne Pellillo Brase
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 4.2, Problem 20P
Residual Plot: Miles per Gallon Consider the data of Problem 9.
(a) Make a residual plot for the least-squares model.
(b) Use the residual plot to comment about the appropriateness of the least- squares model for these data. See Problem 19.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
QUESTION2
The data set provided by JOHN shows the number of yearly values of flood damage relief items represented by y and the annual rainfall (in centimetres) represented by x over a period of 10 years.y(000s) x (cm)4.0 1101.5 2501.2 2203.0 1503.0 4502.5 2002.0 2102.0 2301.1 2903.0 100
(a) Find the standard deviations of x and y.
(b) Find the equation of the least-squares regression line, assuming that the value of the relief items for flood damage depend on the amount of rainfall.
(c) Calculate the correlation coefficient using the…
QUESTION 2
Suppose that you are assigned a task to investigate the relationship between selling price and valuation of plots sold by a local municipality. Data was obtained for a random sample of ten plots.
Plot
Selling price ($'000)
Valuation
1
120
72
2
100
68
3
140
72
4
150
70
5
155
75
6
100
50
7
150
58
8
200
90
9
80
56
10
145
70
Required:
a) Use the method of least squares and estimate the regression equation between selling price and valuation & Provide an interpretation for the slope coefficient?
b) Use the estimated regression equation and make a prediction for a value of the dependent variable when the independent variable is N$ 85 000.
c) Calculate and interpret:
(i) the coefficient of determination?
(ii) Calculate and interpret the correlation coefficient?
Solve the following problems completely.
An article in the Journal of Environmental Engineering (1989, Vol. 115(3), reported the results of a study on the occurrence of sodium and chloride in surface streams in central Rhode Island. The following data are chloride concentration y (in milligrams per liter) and roadway area in the watershed x (in percentage).
Draw a scatter diagram of the data.
Fit the simple linear regression model using the method of least squares. Find an estimate of σ2.
Estimate the mean chloride concentration for a watershed that has 1% roadway area.
Find the fitted value corresponding to x = 0.47 and the associated residual.
Test the hypothesis H0: β1 = 0 versus H1: β1 ≠ 0 using the analysis of variance procedure with α = 0.01.
Find a 99% confidence interval of Mean chloride concentration when roadway area x = 1.0%
Find a 99% prediction interval on chloride concentration when roadway area x = 1.0%.
Plot the residuals versus ŷ and versus x. Interpret these plots.…
Chapter 4 Solutions
Understanding Basic Statistics
Ch. 4.1 - Note: Answers may vary due to rounding....Ch. 4.1 - Note: Answers may vary due to rounding....Ch. 4.1 - Note: Answers may vary due to rounding....Ch. 4.1 - Note: Answers may vary due to rounding....Ch. 4.1 - Critical Thinking: Linear Correlation Look at the...Ch. 4.1 - Critical Thinking: Linear Correlation Look at the...Ch. 4.1 - Critical Thinking: Lurking Variables Over the past...Ch. 4.1 - Critical Thinking: Lurking Variables Over the past...Ch. 4.1 - Critical Thinking: Lurking Variables Over the past...Ch. 4.1 - Critical Thinking: Lurking Variables Over the past...
Ch. 4.1 - Interpretation Trevor conducted a study and found...Ch. 4.1 - Interpretation Do people who spend more time on...Ch. 4.1 - Veterinary Science: Shetland Ponies How much...Ch. 4.1 - Health Insurance:Administrative Cost The following...Ch. 4.1 - Meteorology: Cyclones Can a low barometer reading...Ch. 4.1 - Geology: Earthquakes Is the magnitude of an...Ch. 4.1 - Baseball: Batting Averages and Home Runs In...Ch. 4.1 - University Crime: FBI Report Do larger...Ch. 4.1 - Prob. 19PCh. 4.1 - Prob. 20PCh. 4.1 - Expand Your Knowledge: Using a Table to Test The...Ch. 4.1 - Expand Your Knowledge: Sample Size and...Ch. 4.1 - Prob. 23PCh. 4.2 - Statistical Literacy In the least-squares line...Ch. 4.2 - Statistical Literacy In the least squares line...Ch. 4.2 - Critical Thinking When we use a least-squares line...Ch. 4.2 - Critical Thinking If two variables have a negative...Ch. 4.2 - Critical Thinking: Interpreting Computer Printouts...Ch. 4.2 - Critical Thinking: Interpreting Computer Printouts...Ch. 4.2 - Economics: Entry-Level Jobs An economist is...Ch. 4.2 - Ranching: Cattle You are the foreman of the Bar-S...Ch. 4.2 - Weight of Car: Miles per Gallon Do heavier cars...Ch. 4.2 - Basketball: Fouls Data for this problem are based...Ch. 4.2 - Auto Accidents: Age Data for this problem are...Ch. 4.2 - Auto Accidents: Age Let x be the age of a licensed...Ch. 4.2 - Incoine: Medicai Care Let x be per capita income...Ch. 4.2 - Violent Crimes: Prisons Does prison really deter...Ch. 4.2 - Education: Violent Crime The following data are...Ch. 4.2 - Research: Patents The following data are based on...Ch. 4.2 - Archaeology: Artifacts Data for this problem are...Ch. 4.2 - Cricket Chirps: Temperature Anyone who has been...Ch. 4.2 - Expand Your Knowledge: Residual Plot The...Ch. 4.2 - Residual Plot: Miles per Gallon Consider the data...Ch. 4.2 - Expand Your knowledge: Logarithmic...Ch. 4.2 - Expand Your Knowledge: Logarithmic...Ch. 4.2 - Prob. 24PCh. 4.2 - Expand Your Knowledge: Logarithmic...Ch. 4 - Terminology Consider the equation of a...Ch. 4 - Terminology Consider the values of the sample...Ch. 4 - Terminology Suppose we have a set of ordered pairs...Ch. 4 - Terminology Consider the following terms in a...Ch. 4 - Statistical Literacy Suppose the scatter diagram...Ch. 4 - Critical Thinking Suppose you and a friend each...Ch. 4 - Statistical Literacy When using the least-squares...Ch. 4 - StatisticalLiteracy Suppose that for x = 3. the...Ch. 4 - In Problems 9-14, (a) Draw a scatter diagram for...Ch. 4 - In Problems 9-14, (a) Draw a scatter diagram for...Ch. 4 - In Problems 9-14, (a) Draw a scatter diagram for...Ch. 4 - In Problems 9-14, (a) Draw a scatter diagram for...Ch. 4 - In Problems 9-14, (a) Draw a scatter diagram for...Ch. 4 - In Problems 9-14, (a) Draw a scatter diagram for...Ch. 4 - Prob. 1UTACh. 4 - Prob. 2UTACh. 4 - Prob. 3UTACh. 4 - Prob. 4UTACh. 4 - The data in this section are taken from this...Ch. 4 - The data in this section are taken from this...
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
- Find 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_forwardProblem 2 The following printout shows the results of a simple linear regression model that predicts monthly sales (in thousands of dollars) based on how much money was spent on advertising (in thousands of dollars) during a particular month for 15 stores of a retail chain. a) Is there a statistically significant relationship between money spent on advertising and sales? Test at the 5% level of significance and explain your approach (including hypotheses). b) Somebody claims that every additional $1,000 in advertising will increase sales by more than $2,000 in the population. Can you find support for this claim given the results of your analysis? Test at the 5% level of significance and explain your approach (including hypotheses). How is this test different from the one in part a)? c) Find a 95% confidence interval for the change in sales given a $1,000 increase in the amount of money spent on advertising. How does this confidence interval relate to your answer to part a)?arrow_forward
- Problem 1: I have uploaded data (PCE-PDI.xls) for the US total personal consumption expenditures and total disposable income from 1971:1 to 2009:7. Divide the entire sample into two subsamples: 1971:01 to 1985:12 and 1986:01 to 2009:07. Here consumption expenditure (PCE) is the dependent variable and disposable income (PDI) is the independent variable. Let variable Y denotes consumption expenditure and variable X denotes disposable income. (a) Estimate a two-variable regression model for both subsamples and report the estimated results.arrow_forwardQuestion 9 of 10, Step 1 of 2 The following table lists the birth weights (in pounds), x, and the lengths (in inches), y, for a set of newborn babies at a local hospital. Birth Weights and Lengths Birth Weight (in Pounds), x 8 7 6 9 10 8 3 3 7 11 Length (in Inches), y 20 18 16 21 19 20 15 16 16 21 Step 1 of 2 : Find an equation of the least-squares regression line. Round your answer to three decimal places, if necessary.arrow_forwardQuestion 22: A least squares regression line : A- may be used to predict a value of y if the corresponding x value is given. B- implies a cause-effect relationship between c and y. C- can only be determined if a good linear relationship exists between x and y . D- All of these answers are correct.arrow_forward
- question 2 Shown below are the scatterplots and results of three linear regression analyses done that relate several different behavioural traits to one another in crabs, taken directly from a published paper. The dashed line in each is the line of best fit (least squares regression line). The fitted regression equation, r-value and p-value for each analysis are given in the figure legend below the graphs. Relationships among personality traits in the swimming crab Portunus trituberculatus. Each data point represents an individual crab; data are shown as the specific valye of personality traits (n=88). (A) Relationship between boldness and activity (y=36.04x-17.572, r=0.459, P=0.00). (B) Relationship between activity and hesitancy (y=-0.152x+3.37, r=0.305, P=0.00). (C) Relationship between boldness and hesitancy (y=-1.18x+7.07, r=0.158, P=0.02) For each graph (A – C) and the corresponding results in the figure caption above (A – C), comment on whether the result indicates the null…arrow_forwardStep 1 of 3 : Write the estimated regression equation using the least squares estimates for b0 and b1. Round to four decimal places, if necessary.arrow_forwardquestion 32 Statistics students in Oxnard College sampled 10 textbooks in the Condor bookstore and recorded the number of pages in each textbook and its cost. The bivariate data are shown below: Number of Pages (xx) Cost(yy) 575 95.25 351 60.65 788 137.2 600 108 393 75.95 897 155.55 504 76.6 571 86.65 516 79.4 986 166.9 A student calculates a linear modely = __________x +_____________ . (Please show your answers to two decimal places)Use the model to estimate the cost when number of pages is 829.Cost = $___________- (Please show your answer to 2 decimal places.)arrow_forward
- question 17, chapter 4 residuals part F is what I need help with solving. Hello, I need help solving part F of this problem. X= 30, 40, 50, 60, 70 Y= 82, 77, 72, 64, 52 I found the equation of the line containing points (40, 77) and (70, 52). Y= -5 / 6 X + / 3. Y = negative 5 over 6 times X 331 over 3. the line of least squares regression is y= -73x + 105.9 Part F. Compute the sum of the squared residuals for the line found in part B.arrow_forwardStep 1 of 3: Write the estimated regression equation using the least squares estimates for b0�0 and b1�1. Round to four decimal places, if necessary. Step 2 of 3: What is the mean square error for the model shown in the output? Round to four decimal places, if necessary. Step 3 of 3: What is the standard error for the model shown in the output? Round to four decimal places, if necessary.arrow_forwardAnnual Income. Refer to Problem 18. OutputsA.22(a), (b), and (c) on page A-62 display, respectively, plots of residuals against education, residuals against age, and residuals against predicted income; Output A.22(d) shows a normal probability plot of the residuals. Do these graphs suggest any violations of the assumptions for multiple linear regression inferences for the variables under consideration?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Functions and Change: A Modeling Approach to Coll...
Algebra
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
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