EBK FINITE MATHEMATICS FOR THE MANAGERI
11th Edition
ISBN: 9780100478183
Author: Tan
Publisher: YUZU
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Chapter 1.5, Problem 3TE
To determine
The least-square line for given data.
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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+41.997. A twelfth car weighs 3,425 pounds and gets 13 miles per gallon.
Car Weight (pounds), x Miles per Gallon, y1 3768 202 3987 193 3534 204 3174 225 2580 266 3725 197 2610 258 3780 199 3313 20
10 2997 2711 2753 27a) The coefficient of determination of the expanded data set is R2=nothing%.
2. 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 = – 0.005x+ 38.154. A twelfth car weighs 3,425 pounds and gets
12 miles per gallon. 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 R?
3 Click the icon to view the data table.
%3D
The coefficient of determination of the expanded data set is R =
(Round to one decimal place as needed.)
How does the addition of the twelfth car to the data set affect R?
O A. It increases
R?.
O B. It decreases R.
O C. It does not affect R.
3: Data Table
Weight (pounds), Miles per
Gallon, y
Car 1
3,764
066
3,535
Car 2
22
Car 3
21
Car 4
3,177
21
Car 5
2,576
Car 6
3,725
20
909'
3,775
Car 7
Car 8
61-
21
Car 9
3,311
Car 10
2,993
Car 11
2,759
25
The scatterplot below shows Olympic gold medal performances in the long jump from 1900 to 1988. The long jump is measured in meters.
Here is the equation of the least squares regression linePredicted long jump = 7.24 + 0.014 * year since 1900.
What does the vertical-intercept (a.k.a. y-intercept) tell us?
Chapter 1 Solutions
EBK FINITE MATHEMATICS FOR THE MANAGERI
Ch. 1.1 - What can you say about the signs of a and b if the...Ch. 1.1 - Refer to the accompanying figure. a. Given the...Ch. 1.1 - Prob. 1ECh. 1.1 - Prob. 2ECh. 1.1 - Prob. 3ECh. 1.1 - Prob. 4ECh. 1.1 - Prob. 5ECh. 1.1 - Prob. 6ECh. 1.1 - In Exercises 712, refer to the accompanying...Ch. 1.1 - Prob. 8E
Ch. 1.1 - Prob. 9ECh. 1.1 - Prob. 10ECh. 1.1 - Prob. 11ECh. 1.1 - In Exercises 712, refer to the accompanying...Ch. 1.1 - Prob. 13ECh. 1.1 - Prob. 14ECh. 1.1 - Prob. 15ECh. 1.1 - Prob. 16ECh. 1.1 - Prob. 17ECh. 1.1 - Prob. 18ECh. 1.1 - Prob. 19ECh. 1.1 - Prob. 20ECh. 1.1 - Prob. 21ECh. 1.1 - In Exercises 2124, find the distance between the...Ch. 1.1 - In Exercises 2124, find the distance between the...Ch. 1.1 - Prob. 24ECh. 1.1 - Find the coordinates of the points that are 10...Ch. 1.1 - Find the coordinates of the points that are 5...Ch. 1.1 - Show that the points (3,4), (3,7), (6,1) and (0,2)...Ch. 1.1 - Show that the triangle with vertices (5,2), (2,5),...Ch. 1.1 - Prob. 29ECh. 1.1 - Prob. 30ECh. 1.1 - Prob. 31ECh. 1.1 - Prob. 32ECh. 1.1 - Prob. 33ECh. 1.1 - Prob. 34ECh. 1.1 - TRACKING A CRIMINAL WITH GPS After obtaining a...Ch. 1.1 - PLANNING A GRAND TOUR A grand tour of four cities...Ch. 1.1 - WILL YOU INCUR A DELIVERY CHARGE? A furniture...Ch. 1.1 - OPTIMIZING TRAVEL TIME Towns A, B, C, and D are...Ch. 1.1 - MINIMIZING SHIPPING COSTS FOR A FLEET OF AUTOS...Ch. 1.1 - Prob. 40ECh. 1.1 - PURCHASING AN HDTV ANTENNA Will Barclay wishes to...Ch. 1.1 - DISTANCE BETWEEN TWO CRUISE SHIPS Two cruise ships...Ch. 1.1 - DISTANCE BETWEEN TWO CARGO SHIPS Sailing north at...Ch. 1.1 - WATHING A ROCKET LAUNCH At a distance of 4000 ft...Ch. 1.1 - a. Show that the midpoint of the line segment...Ch. 1.1 - A SCAVENGER HUNT A tree is located 20 yd to the...Ch. 1.1 - Prob. 47ECh. 1.1 - Prob. 48ECh. 1.1 - Let (x1,y1) and (x2,y2) be two points lying in the...Ch. 1.1 - In the Cartesian coordinate system, the two axes...Ch. 1.2 - What is the slope of a nonvertical line? What can...Ch. 1.2 - Give a point-slope form, b the slope-intercept...Ch. 1.2 - Prob. 3CQCh. 1.2 - Prob. 4CQCh. 1.2 - Prob. 1ECh. 1.2 - In Exercises 14, find the slope of the line shown...Ch. 1.2 - Prob. 3ECh. 1.2 - Prob. 4ECh. 1.2 - Prob. 5ECh. 1.2 - For Exercises 510, find the slope of the line that...Ch. 1.2 - Prob. 7ECh. 1.2 - Prob. 8ECh. 1.2 - Prob. 9ECh. 1.2 - In Exercise 5-10, find the slope of the line that...Ch. 1.2 - Prob. 11ECh. 1.2 - Given the equation 2x+3y=4, answer the following...Ch. 1.2 - Prob. 13ECh. 1.2 - Prob. 14ECh. 1.2 - Prob. 15ECh. 1.2 - Prob. 16ECh. 1.2 - Prob. 17ECh. 1.2 - Prob. 18ECh. 1.2 - In Exercises 19 and 20, determine whether the...Ch. 1.2 - Prob. 20ECh. 1.2 - If the line passing through the points (1,a) and...Ch. 1.2 - If the line passing through the points (a,1) and...Ch. 1.2 - In Exercises 2326, find an equation of the line...Ch. 1.2 - In Exercises 2326, find an equation of the line...Ch. 1.2 - In Exercises 2326, find an equation of the line...Ch. 1.2 - Prob. 26ECh. 1.2 - In Exercises 2730, find an equation of the line...Ch. 1.2 - Prob. 28ECh. 1.2 - In Exercises 2730, find an equation of the line...Ch. 1.2 - Prob. 30ECh. 1.2 - In Exercises 31 and 32, determine whether the...Ch. 1.2 - Prob. 32ECh. 1.2 - In Exercises 3336, find an equation of line that...Ch. 1.2 - Prob. 34ECh. 1.2 - In Exercises 3336, find an equation of line that...Ch. 1.2 - Prob. 36ECh. 1.2 - In Exercise 3742, write the equation in the...Ch. 1.2 - Prob. 38ECh. 1.2 - In Exercise 3742, write the equation in the...Ch. 1.2 - Prob. 40ECh. 1.2 - In Exercise 3742, write the equation in the...Ch. 1.2 - Prob. 42ECh. 1.2 - Find an equation of the horizontal line that...Ch. 1.2 - Find an equation of the vertical line that passes...Ch. 1.2 - Prob. 45ECh. 1.2 - Prob. 46ECh. 1.2 - Find an equation of the line that passes through...Ch. 1.2 - Find an equation of the line that passes through...Ch. 1.2 - Prob. 49ECh. 1.2 - Prob. 50ECh. 1.2 - Prob. 51ECh. 1.2 - Prob. 52ECh. 1.2 - In Exercises 5156, find an equation of the line...Ch. 1.2 - Prob. 54ECh. 1.2 - In Exercises 51-56, find an equation of the line...Ch. 1.2 - Prob. 56ECh. 1.2 - Given that the point P(3,5) lies on the line...Ch. 1.2 - Prob. 58ECh. 1.2 - In Exercises 5964, sketch the straight line...Ch. 1.2 - Prob. 60ECh. 1.2 - In Exercises 5964, sketch the straight line...Ch. 1.2 - Prob. 62ECh. 1.2 - Prob. 63ECh. 1.2 - Prob. 64ECh. 1.2 - Prob. 65ECh. 1.2 - Prob. 66ECh. 1.2 - Prob. 67ECh. 1.2 - Prob. 68ECh. 1.2 - Prob. 69ECh. 1.2 - Prob. 70ECh. 1.2 - Prob. 71ECh. 1.2 - John claims that the following points lie on a...Ch. 1.2 - Prob. 73ECh. 1.2 - Prob. 74ECh. 1.2 - NUCLEAR PLANT UTILIZATION The United States is not...Ch. 1.2 - Prob. 76ECh. 1.2 - COLLEGE ADMISSIONS Using data compiled by the...Ch. 1.2 - WEIGHT OF WHALES The equation W=3.51L192,...Ch. 1.2 - Prob. 79ECh. 1.2 - DECLINING NUMBER OF PAY PHONES As cell phones...Ch. 1.2 - Prob. 81ECh. 1.2 - IDEAL HEIGHTS AND WEIGHTS FOR WOMEN The Venus...Ch. 1.2 - Prob. 83ECh. 1.2 - CORPORATE FRAUD The number of pending corporate...Ch. 1.2 - Prob. 85ECh. 1.2 - Prob. 86ECh. 1.2 - Is there a difference between the statements "The...Ch. 1.2 - Prob. 88ECh. 1.2 - Prob. 89ECh. 1.2 - Prob. 90ECh. 1.2 - Prob. 91ECh. 1.2 - Prob. 92ECh. 1.2 - Prob. 93ECh. 1.2 - Prob. 94ECh. 1.2 - Prob. 95ECh. 1.2 - Prove that if a line L1 with slope m1 is...Ch. 1.2 - Prob. 1TECh. 1.2 - Prob. 2TECh. 1.2 - Prob. 3TECh. 1.2 - Prob. 4TECh. 1.2 - Prob. 5TECh. 1.2 - Prob. 6TECh. 1.2 - Prob. 7TECh. 1.2 - Prob. 8TECh. 1.2 - Prob. 9TECh. 1.2 - Prob. 10TECh. 1.2 - Prob. 11TECh. 1.2 - Prob. 12TECh. 1.3 - a. What is a function? Give an example. b. What is...Ch. 1.3 - What is the general form of a linear cost...Ch. 1.3 - Is the slope of a linear demand curve positive or...Ch. 1.3 - The value of an investment in dollars after t...Ch. 1.3 - In Exercises 110, determine whether the equation...Ch. 1.3 - In Exercises 110, determine whether the equation...Ch. 1.3 - In Exercises 110, determine whether the equation...Ch. 1.3 - Prob. 4ECh. 1.3 - In Exercises 110, determine whether the equation...Ch. 1.3 - Prob. 6ECh. 1.3 - In Exercises 110, determine whether the equation...Ch. 1.3 - In Exercises 110, determine whether the equation...Ch. 1.3 - In Exercises 110, determine whether the equation...Ch. 1.3 - In Exercises 110, determine whether the equation...Ch. 1.3 - A manufacturer has a monthly fixed cost of 40,000...Ch. 1.3 - A manufacturer has a monthly fixed cost of 10,000...Ch. 1.3 - Find the constants m and b in the linear function...Ch. 1.3 - Find the constants m and b in the linear function...Ch. 1.3 - Prob. 15ECh. 1.3 - Prob. 16ECh. 1.3 - CONSUMPTION FUNCTIONS A certain economys...Ch. 1.3 - SALES TAX In a certain state, the sales tax T on...Ch. 1.3 - SOCIAL SECURITY COLAs Social Security recipients...Ch. 1.3 - PROFIT FUNCTION FOR DIGITAL TIMERS Auto Time, a...Ch. 1.3 - PROFIT FUNCTION FOR LIGHT BULBS The management of...Ch. 1.3 - Prob. 22ECh. 1.3 - Prob. 23ECh. 1.3 - LINEAR DEPRECIATION Suppose an asset has an...Ch. 1.3 - LINEAR DEPRECIATION OF AN OFFICE BUILDING Rework...Ch. 1.3 - Prob. 26ECh. 1.3 - DRUG DOSAGES FOR CHILDREN A method sometime used...Ch. 1.3 - DRUG DOSAGES FOR CHILDREN Cowlings Rule is a...Ch. 1.3 - DRINKING AND DRIVING AMONG HIGH SCHOOL STUDENTS...Ch. 1.3 - CALIFORNIA EMISSIONS CAPS The California emissions...Ch. 1.3 - Prob. 31ECh. 1.3 - U.S. AIRPLANE PASSENGER PROJECTIONS In a report...Ch. 1.3 - CELSIUS AND FAHRENHEIT TEMPERATURES The...Ch. 1.3 - CRICKET CHIRPING AND TEMPERATURE Entomologists...Ch. 1.3 - Prob. 35ECh. 1.3 - Prob. 36ECh. 1.3 - Prob. 37ECh. 1.3 - Prob. 38ECh. 1.3 - DEMAND FUNCTION FOR A COMMODITY At a unit price...Ch. 1.3 - Prob. 40ECh. 1.3 - DEMAND FUNCTION FOR A COMMODITY Assume that a...Ch. 1.3 - DEMAND FUNCTION FOR A SPORTS WATCH The demand...Ch. 1.3 - Prob. 43ECh. 1.3 - Prob. 44ECh. 1.3 - Prob. 45ECh. 1.3 - Prob. 46ECh. 1.3 - SUPPLY FUNCTION FOR A DIGITAL RECORDER Suppliers...Ch. 1.3 - SUPPLY FUNCTION FOR A REFRIGERATOR Producers of a...Ch. 1.3 - DEMAND FOR WIRELESS LOUDSPEAKERS The demand...Ch. 1.3 - DEMAND FORWASHABLE COMPUTER KEYBOARDS The demand...Ch. 1.3 - Prob. 51ECh. 1.3 - Prob. 52ECh. 1.3 - Prob. 53ECh. 1.3 - Prob. 54ECh. 1.3 - Prob. 1TECh. 1.3 - Prob. 2TECh. 1.3 - Prob. 3TECh. 1.3 - Prob. 4TECh. 1.3 - Prob. 5TECh. 1.3 - Prob. 6TECh. 1.3 - Prob. 7TECh. 1.3 - Prob. 8TECh. 1.4 - Explain why you would expect that the intersection...Ch. 1.4 - In the accompanying figure, C(x) is the cost...Ch. 1.4 - The accompanying figure gives the demand curve and...Ch. 1.4 - In Exercises 16, find the point of intersection of...Ch. 1.4 - In Exercises 16, find the point of intersection of...Ch. 1.4 - In Exercises 16, find the point of intersection of...Ch. 1.4 - In Exercises 16, find the point of intersection of...Ch. 1.4 - In Exercises 1-6, find the point of intersection...Ch. 1.4 - In Exercises 16, find the point of intersection of...Ch. 1.4 - In Exercises 710, find the break-even point for...Ch. 1.4 - In Exercises 710, find the break-even point for...Ch. 1.4 - In Exercises 710, find the break-even point for...Ch. 1.4 - In Exercises 710, find the break-even point for...Ch. 1.4 - BREAK-EVEN ANALYSIS Auto Time, a manufacturer of...Ch. 1.4 - BREAK-EVEN ANALYSIS A division of Carter...Ch. 1.4 - BREAK-EVEN ANALYSIS A division of the Gibson...Ch. 1.4 - LEASING A TRUCK Ace Truck Leasing Company leases a...Ch. 1.4 - DECISION ANALYSIS A product may be made by using...Ch. 1.4 - ANNUAL SALES OF TWO PHARMACIES The annual sales of...Ch. 1.4 - LCDs VERSUS CRTs The global shipments of...Ch. 1.4 - DIGITAL VERSUS FILM CAMERAS The sales of digital...Ch. 1.4 - U.S. FINANCIAL TRANSACTIONS The percentage of U.S....Ch. 1.4 - BROADBAND VERSUS DIAL-UP The number of U.S....Ch. 1.4 - Prob. 21ECh. 1.4 - For each pair of supply-and-demand equations in...Ch. 1.4 - Prob. 23ECh. 1.4 - Prob. 24ECh. 1.4 - EQUILIBRIUM QUANTITY AND PRICE FOR DVD PLAYERS The...Ch. 1.4 - EQUILIBRIUM QUANTITY AND PRICE FOR GPS NAVIGATORS...Ch. 1.4 - 27. EQUILIBRIUM QUANTITY AND PRICE FOR TABLET...Ch. 1.4 - 28. EQUILIBRIUM QUANTITY AND PRICE FOR ESPRESSO...Ch. 1.4 - EQUILIBRIUM QUANTITY AND PRICE FOR WIRELESS...Ch. 1.4 - Prob. 30ECh. 1.4 - Suppose the demand and supply equations for a...Ch. 1.4 - Suppose the cost function associated with a...Ch. 1.4 - In Exercises 33 and 34, determine whether the...Ch. 1.4 - Prob. 34ECh. 1.4 - Let L1 and L2 be two nonvertical straight lines in...Ch. 1.4 - Prob. 36ECh. 1.4 - Prob. 1TECh. 1.4 - Prob. 2TECh. 1.4 - Prob. 3TECh. 1.4 - Prob. 4TECh. 1.4 - Prob. 5TECh. 1.4 - Prob. 6TECh. 1.4 - Prob. 7TECh. 1.4 - BREAK-EVEN ANALYSIS The Monde Company makes a wine...Ch. 1.4 - Prob. 9TECh. 1.4 - Prob. 10TECh. 1.4 - Prob. 11TECh. 1.4 - Prob. 12TECh. 1.5 - Explain the terms (a) scatter diagram (b)...Ch. 1.5 - Prob. 2CQCh. 1.5 - Prob. 1ECh. 1.5 - Prob. 2ECh. 1.5 - Prob. 3ECh. 1.5 - Prob. 4ECh. 1.5 - Prob. 5ECh. 1.5 - In Exercises 16, a find the equation of the least...Ch. 1.5 - COLLEGE ADMISSIONS The accompanying data were...Ch. 1.5 - Prob. 8ECh. 1.5 - Prob. 9ECh. 1.5 - Prob. 10ECh. 1.5 - Prob. 11ECh. 1.5 - Prob. 12ECh. 1.5 - Prob. 13ECh. 1.5 - Prob. 14ECh. 1.5 - Prob. 15ECh. 1.5 - Prob. 16ECh. 1.5 - Prob. 17ECh. 1.5 - Prob. 18ECh. 1.5 - Prob. 19ECh. 1.5 - Prob. 20ECh. 1.5 - Prob. 21ECh. 1.5 - Prob. 22ECh. 1.5 - BOUNCED-CHECK CHARGES Overdraft fees have become...Ch. 1.5 - Prob. 24ECh. 1.5 - Prob. 25ECh. 1.5 - Prob. 26ECh. 1.5 - Prob. 27ECh. 1.5 - Prob. 28ECh. 1.5 - Prob. 29ECh. 1.5 - Prob. 30ECh. 1.5 - Prob. 1TECh. 1.5 - Prob. 2TECh. 1.5 - Prob. 3TECh. 1.5 - Prob. 4TECh. 1.5 - Prob. 5TECh. 1.5 - Prob. 6TECh. 1.5 - Prob. 7TECh. 1.5 - Prob. 8TECh. 1.5 - Prob. 9TECh. 1.5 - Prob. 10TECh. 1.CRQ - Prob. 1CRQCh. 1.CRQ - Prob. 2CRQCh. 1.CRQ - Prob. 3CRQCh. 1.CRQ - Prob. 4CRQCh. 1.CRQ - Prob. 5CRQCh. 1.CRQ - Prob. 6CRQCh. 1.CRQ - Prob. 7CRQCh. 1.CRQ - Prob. 8CRQCh. 1.CRQ - Prob. 9CRQCh. 1.CRQ - Prob. 10CRQCh. 1.CRQ - Prob. 11CRQCh. 1.CRQ - Prob. 12CRQCh. 1.CRE - Prob. 1CRECh. 1.CRE - Prob. 2CRECh. 1.CRE - Prob. 3CRECh. 1.CRE - Prob. 4CRECh. 1.CRE - Prob. 5CRECh. 1.CRE - Prob. 6CRECh. 1.CRE - Prob. 7CRECh. 1.CRE - Prob. 8CRECh. 1.CRE - Prob. 9CRECh. 1.CRE - Prob. 10CRECh. 1.CRE - Prob. 11CRECh. 1.CRE - Prob. 12CRECh. 1.CRE - Prob. 13CRECh. 1.CRE - Prob. 14CRECh. 1.CRE - Prob. 15CRECh. 1.CRE - Prob. 16CRECh. 1.CRE - Prob. 17CRECh. 1.CRE - Prob. 18CRECh. 1.CRE - Prob. 19CRECh. 1.CRE - Prob. 20CRECh. 1.CRE - Prob. 21CRECh. 1.CRE - Prob. 22CRECh. 1.CRE - Prob. 23CRECh. 1.CRE - Prob. 24CRECh. 1.CRE - Prob. 25CRECh. 1.CRE - Prob. 26CRECh. 1.CRE - PROFIT FUNCTION FOR DISPOSABLE CAMERAS A company...Ch. 1.CRE - Prob. 28CRECh. 1.CRE - Prob. 29CRECh. 1.CRE - Prob. 30CRECh. 1.CRE - SUPPLY EQUATION FOR BYCYCLES Bicycle suppliers...Ch. 1.CRE - DEMAND FOR EARBUD HEADPHONES The demand equation...Ch. 1.CRE - Prob. 33CRECh. 1.CRE - Prob. 34CRECh. 1.CRE - Prob. 35CRECh. 1.CRE - Prob. 36CRECh. 1.CRE - Prob. 37CRECh. 1.CRE - Prob. 38CRECh. 1.CRE - MARKET EQUILIBRIUM FOR REFRIGERATORS The demand...Ch. 1.CRE - Prob. 40CRECh. 1.CRE - EQUILIBRIUM QUANTITY AND PRICE FOR EARBUD...Ch. 1.CRE - Prob. 42CRECh. 1.BMO - Plot the points A(2,1) and B(3,4) on the same set...Ch. 1.BMO - Prob. 2BMOCh. 1.BMO - Prob. 3BMOCh. 1.BMO - Prob. 4BMOCh. 1.BMO - Prob. 5BMOCh. 1.BMO - Prob. 6BMO
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- Cellular Phone Subscribers The table shows the numbers of cellular phone subscribers y in millions in the United States from 2008 through 2013. Source: CTIA- The Wireless Association Year200820092010201120122013Number,y270286296316326336 (a) Find the least squares regression line for the data. Let x represent the year, with x=8 corresponding to 2008. (b) Use the linear regression capabilities of a graphing utility to find a linear model for the data. How does this model compare with the model obtained in part a? (c) Use the linear model to create a table of estimated values for y. Compare the estimated values with the actual data.arrow_forwardThe 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) The coefficient of determination of the expanded data set is R = %. (Round to one decimal place as needed.) Data Table How does the addition of the twelfth car to the data set affect R? Miles per Weight |(pounds), x A. It increases R. Gallon, y Car 1 3,771 22 B. It decreases R2. Car 2 3,990 19 C. It does not affect R2. 3,534 Car 3 20 Car 4 3,172 24 (b) Is the point corresponding to the twelfth car influential? Is it an outlier? Car 5 2,579 27 Car 6 3,730 20 A. No, it is not influential. Yes, it is an outlier. Car 7 2,605 25 B. Yes, it is influential. No, it is not an outlier. Car 8 3,777 19 C. No, it is not influential. No, it is not an outlier. Car 9 3,308 19 D. Yes, it is influential. Yes, it is an outlier. Car…arrow_forwardA candy maker surveyed chocolate bars available in a local supermarket and found the least squares regression model shown below. Use the model to answer parts a through c below. Calories = 28.9+ 12.65Fat(g) +2.41Sugar(g) a) The hand-crafted chocolate she makes has 15g of fat and 20g of sugar. How many calories does the model predict for a serving? calories (Type an integer or a decimal. Do not round.) b) In fact, a laboratory test shows that her candy has 248 calories per serving. Find the residual corresponding to this candy. calories (Type an integer or a decimal. Do not round.) c) What does that residual say about her candy? Choose the correct choice below and fill in the answer box within your choice. (Type an integer or a decimal. Do not round.) OA. Her candy has OB. Her candy has more calories than might be expected from the model. fewer calories than might be expected from the model.arrow_forward
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