The data in the table represent the weights of various domestic cars and their miles per gallon in the city for the 2008 model year. For these data,the least-squares regression line is y = - 0.006x+ 41.337. A twelfth car weighs 3,425 pounds and gets 12 miles per gallon.(a) Compute the coefficient of determination of the expanded data set. What effect does the addition of the twelfth car to the data set have onR?(b) Is the point corresponding to the twelfth car influential? Is it an outlier?Click the icon to view the data table.Data Table.....Weight(pounds), xMiles per(a) The coefficient of determination of the expanded data set is R = %.Gallon, y(Round to one decimal place as needed.)Car 13,77122Car 2,99019Car 33,53420Car 43,17224Car 52,57927Car 63,73020Car 72,60525Car 83,77719Car 93,30819Car 102,99726Car 112,75127

The least-square regression equation is given as: y^=-0.006x+41.337 The slope of the regression…

Answered: The data in the table represent the…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The data in the table represent the weights of various domestic cars and their miles per gallon in the city for the 2008 model year. For these data, the least-squares regression line is y = - 0.006x + 43.875. A twelfth car weighs 3,425 pounds and gets 13 miles per gallon. (a) Compute the coefficient of determination of the expanded data set. What effect does the addition of the twelfth car to the data set have on R2? (b) Is the point corresponding to the twelfth car influential? Is it an outlier? Data Table Click the icon to view the data table. Weight |(pounds), x Miles per Gallon, y Car 1 3,770 20 Car 2 3,980 19 Car 3 3,530 19 Car 4 3,175 22 Car 5 2,580 27 Car 6 3,729 20 Car 7 2,607 26 Car 8 3,776 19 Car 9 3,311 22 Car 10 2,999 27 Car 11 2,755 27
Is It Getting Harder to Win a Hot Dog Eating Contest?Every Fourth of July, Nathan’s Famous in New York City holds a hot dog eating contest. The table below shows the winning number of hot dogs and buns eaten every year from 2002 to 2015, and the data are also available in HotDogs. The figure below shows the scatterplot with the regression line. Year Hot Dogs 2015 62 2014 61 2013 69 2012 68 2011 62 2010 54 2009 68 2008 59 2007 66 2006 54 2005 49 2004 54 2003 45 2002 50 Winning number of hot dogs in the hot dog eating contest Winning number of hot dogs and buns Click here for the dataset associated with this question. (a) Is the trend in the data mostly positive or negative? Positive Negative (b) Using the figure provided, is the residual larger in 2007 or 2008?Choose the answer from the menu in accordance to item (b) of the question statement 20072008 Is the residual positive or…
The following regression model was estimated. Q is the number of meals served, P is the average price per meal (customer ticket amount, in dollars), Rxis the average price charged by competitors (in dollars), Ad is the local advertising budget for each outlet (in dollars), and I is the average income per household in each outlet's immediate service area. Least squares estimation of the regression equation on the basis of the 25 data observations resulted in the estimated regression coefficients and other statistics given in Table below. Variable Coefficient Standard Error of Coefficient Intercept 128832.240 69974.818 Price (P) Competitor Price (Px) | Advertising (Ad) Income () -19875.954 4100.856 15467.936 459.280 0.261 0.094 8.780 1.017 Coefficient of determination R =83.3% (a) Interpret the coefficients of independent variables. (b) Test the significance of independent variables at 5% level of Significance. (c) Interpret R? with the help of adjusted R2. (d) Test for the overall…
Suppose Tatiyana is interested in the relationship between language ability and time spent reading. She randomly selects a sample of 30 students from the local high school and collects their scores from a language aptitude test. She surveys the sample asking each student how many hours per month he or she spends reading. Using the sample data, Tatiyana produces a scatterplot with reading time on the horizontal axis and language test scores on the vertical axis. She develops a least squares regression equation where ? is the amount of time spent reading during the month and ?̂ is the predicted value of the language test score. ?̂=3.251x+31.237 Compute the value of ?̂ when a student spends 42 hours reading. Give your answer precise to one decimal place. Avoid rounding until the last step. ?̂= ? points Identify all of the true statements regarding the interpretation of ?̂ when ?=42. The value of ?̂ is ? a. the predicted number of students that read for 42 hours. b. the language test…
In baseball, two statistics, the ERA (Earned Run Average) and the WHIP (Walks and Hits per Inning Pitched), are used to measure the quality of pitchers. For both measures, smaller values indicate higher quality. The following computer output gives the results from predicting ERA by using WHIP in a least-squares regression for the 2017 baseball season. Variable DF Estimate SE T Intercept 1 -5.0 0.26 - 19.3 WHIP 1 6.8 0.14 47.4 Which of the following statements is the best interpretation of the value 6.8 shown in the output? ERA is predicted to increase by 6.8 units for each 1 unit increase of WHIP. WHIP is predicted to increase by 6.8 units for each 1 unit increase of ERA. For a pitcher with 0 units of WHIP, the ERA is predicted to be approximately 6.8 units. For a pitcher with 0 units of ERA, the WHIP is predicted to be approximately 6.8 units. Approximately 6.8% of the variability in ERA is due to its linear relationship with WHIP.
The data in the table represent the number of licensed drivers in various age groups and the number of fatal accidents within the age group by gender. Complete parts (a) to (c) below. Click the icon to view the data table. C... (a) Find the least-squares regression line for males treating the number of licensed drivers as the explanatory variable, x, and the number of fatal crashes, y, as the response variable. Repeat this procedure for female Find the least-squares regression line for males. ŷ=0x+0 (Round the slope to three decimal places and round the constant to the nearest integer as needed.) Data for licensed drivers by age and gender. 21-24 25-34 35-44 45-54 55-64 65-74 > 74 Number of Male Fatal Licensed Age Drivers (000s) < 16 12 16-20 6,424 6,914 18,068 20,406 Number of Number of Female Fatal Crashes Licensed (Males) Drivers (000s) 227 12 6,139 Crashes (Females) 77 2,113 1,534 5,180 5,016 6,816 8,567 17,664 2,780 7,990 20,047 2,742 19,984 14,441 8,386 5,375 19,898 14,328 8,194…
Report the equation of the regression line and interpret it in the context of the problem
Draw a graph of the least-squares regression line on your scatterplot. (For hand-drawing, round the slope and y-intercept to one decimal place before drawing the line.) Be sure to show how you were able to plot the line starting with its equation. Model City Miles per Gallon Highway Miles per Gallon Acura RLX 20 29 BMW 530i 24 34 Buick LaCrosse eAssist 25 35 Chevrolet Malibu 29 36 Ford Hybrid FWD 43 41 Honda Civic 32 42 Infiniti Q50 Red Sport 20 26 Kia Forte 30 40 Lexus ES 350 22 33 Mercedes Benz AMG S 21 30 Mini Cooper Clubman 24 32 Nissan Maxima 20 30 Suburu Legacy AWD 25 34 Toyota Prius ECO 58 53
Yummy Lunch Restaurant needs to decide the most profitable location for their business expansion. Marketing manager plans to use a multiple regression model to achieve their target. His model considers yearly revenue as the dependent variable. He found that number of people within 2KM (People), Mean household income(income), no of competitors and price as explanatory variables of company yearly revenue. The following is the descriptive statistics and regression output from Excel. Revenue People Income Competitors Price Mean 343965.68 5970.26 41522.96 2.8 5.68 Standard Error 5307.89863 139.0845281 582.1376385 0.142857 0.051030203 Median 345166.5 6032 41339.5 3 5.75 Mode #N/A 5917 #N/A 3 6 Standard Deviation 37532.51115 983.47613 4116.334718 1.010153 0.360838027 Sample Variance 1408689393 967225.2984 16944211.51 1.020408 0.130204082 Sum 17198284 298513 2076148…
Biologist Theodore Garland, Jr. studied the relationship between running speeds and morphology of 49 species of cursorial mammals (mammals adapted to or specialized for running). One of the relationships he investigated was maximal sprint speed in kilometers per hour and the ratio of metatarsal-to-femur length. A least-squares regression on the data he collected produces the equation ŷ = 37.67 + 33.18x %3D where x is metatarsal-to-femur ratio and ŷ is predicted maximal sprint speed in kilometers per hour. The standard error of the intercept is 5.69 and the standard error of the slope is 7.94. Construct an 80% confidence interval for the slope of the population regression line. Give your answers precise to at least two decimal places. Lower limit: Upper limit:
An article gave data on a measure of pollution (in micrograms of particulate matter per cubic meter of air) and the cost of medical care per person over age 65 for six geographical regions of the United States. Find the equation of the least-squares line describing the relationship between y = medical cost and x = pollution. (Give the answer to two decimal places.) ŷ = Region North eBook Upper South Deep South West South Big Sky West Additional Materials Pollution Cost of Medical 30.0 922 31.8 898 32.1 975 26.8 979 30.4 959 40.0 906
Yummy Lunch Restaurant needs to decide the most profitable location for their business expansion. Marketing manager plans to use a multiple regression model to achieve their target. His model considers yearly revenue as the dependent variable. He found that number of people within 2KM (People), Mean household income(income), no of competitors and price as explanatory variables of company yearly revenue. The following is the descriptive statistics and regression output from Excel. Revenue People Income Competitors Price Mean 343965.68 5970.26 41522.96 2.8 5.68 Standard Error 5307.89863 139.0845281 582.1376385 0.142857 0.051030203 Median 345166.5 6032 41339.5 3 5.75 Mode #N/A 5917 #N/A 3 6 Standard Deviation 37532.51115 983.47613 4116.334718 1.010153 0.360838027 Sample Variance 1408689393 967225.2984 16944211.51 1.020408 0.130204082 Sum 17198284 298513 2076148 140…

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