Consider Again the Cigarette Consumption Data Described Regression Analysis
Problem 1
Cereals For many people, breakfast cereal is an important source of fiber in their diets. Cereals also contain potassium, a mineral shown to be associated with maintaining a healthy blood pressure. An analysis of the amount of fiber (in grams) and the potassium content (in milligrams) in servings of 77 breakfast cereals produced the regression model $\overline{\text {Potassium}}=38+27$ Fiber. If your cereal provides ix grams of fiber per serving, how much potassium does the model estimate y'all will go?
Sophie K.
Numerade Educator
Problem two
Horsepower A study that examined the relationship between the fuel economy (mpg) and horsepower for 15 models of cars produced the regression model $\widehat{thou p g}=46.87-0.084 H P .$ If the car you are thinking
Problem iii
More cereal Exercise 1 describes a regression model thas estimates a cereal's potassium content from the amount of fiber it contains. In this context, what does it mean to say that a cereal has a negative residue?
Problem 4
Horsepower, again Practise two describes a regression model that uses a car's horsepower to judge its fuel economy. In this context, what does it hateful to say that a certain motorcar has a positive residual?
Sophie K.
Numerade Educator
Trouble 5
Some other bowl In Exercise $1,$ the regression model Potassium $=38+27$ Fiber relates fiber (in grams) and potassium content (in milligrams) in servings of break fast cereals. Explain what the slope means.
Problem half dozen
More horsepower In Exercise $2,$ the regression model $\widehat{thou p yard}=46.87-0.084 \mathrm{HP}$ relates cars' horsepower to their fuel economy (in mpg). Explain what the slope
ways.
Trouble 7
Cereal again The correlation between a cereal's fiber and potassium contents is $r=0.903 .$ What fraction of the variability in potassium is deemed for by the corporeality of fiber that servings contain?
Sophie K.
Numerade Educator
Problem 8
Another car The correlation between a car'due south horsepower and its fuel economic system (in mpg) is $r=-0.869 .$ What fraction of the variability in fuel economic system is accounted for by the horsepower?
Sophie K.
Numerade Educator
Problem nine
Last bowl! For Exercise 1's regression model predicting potassium content (in milligrams) from the corporeality of cobweb (in grams) in breakfast cereals, $s_{e}=30.77 .$ Explain in this context what that means.
Sophie K.
Numerade Educator
Trouble ten
Concluding tank! For Exercise ii 'due south regression model predicting fuel economic system (in mpg) from the auto's horsepower, $s_{e}=3.287 .$ Explain in this context what that ways.
Sophie K.
Numerade Educator
Problem 11
Residuals I Tell what each of the residual plots below indicates nigh the appropriateness of the linear model that was fit to the data.
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Sophie Thou.
Numerade Educator
Problem 12
Residuals II Tell what each of the balance plots below indicates well-nigh the appropriateness of the linear model that was fit to the data.
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Trouble thirteen
What gradient I? If y'all create a regression model for predicting the Weight of a car (in pounds) from its Length (in feet), is the slope most probable to exist $iii,30,300,$ or $3000 ?$ Explain.
Sophie K.
Numerade Educator
Problem 14
What slope II? If you create a regression model for estimating the Peak of a pine tree (in feet) based on the Circumference of its trunk (in inches), is the slope most likely to be 0.1, 1, 10, or 100? Explain.
Problem 15
True or faux If false, explain briefly.
a) Nosotros choose the linear model that passes through the most data points on the scatter plot.
b) The residuals are the observed $y$ -values minus the $y$ -values predicted by the linear model.
c) Least squares means that the foursquare of the largest residual
Problem 16
True or imitation III If false, explain briefly.
a) Some of the residuals from a to the lowest degree squares linear model will be positive and some will be negative.
b) Least Squares ways that some of the squares of the residuals are minimized.
c) We write $\hat{y}$ to announce the predicted values and $y$ to denote the observed values.
Problem 17
Bookstore sales revisited Recall the data we saw in Chapter $6,$ Exercise iii for a bookstore. The director wants to predict Sales from Number of Sales People Working.
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a) Write the regression equation. Ascertain the variables used in your equation.
b) What does the slope hateful in this context?
c) What does the $y$ -intercept mean in this context? Is it meaningful?
d) If 18 people are working, what Sales exercise you predict?
east) If sales for the 18 people are actually $\$ 25,000,$ what is the value of the rest?
f) Have nosotros overestimated or underestimated the sales?
Problem 18
Disk drives once more In Chapter $6,$ Exercise $4,$ nosotros saw some information on hard drives. After correcting for an outlier, these data look like this: we desire to predict Price from Capacity.
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a) Write the regression equation. Define the variables used in your equation.
b) What does the slope hateful in this context?
c) What does the $y$ -intercept hateful in this context? Is it meaningful?
d) What would you lot predict for the price of a three.0 TB bulldoze?
e) You found a 3.0 TB drive for $\$ 300 .$ Is this a good buy? How much would you lot relieve compared to what you lot expected to buy?
f) Does the model overestimate or underestimate the price for a three.0 TB drive?
Trouble 19
Bookstore sales once more Hither are the residuals for a regression of Sales on Number of Sales People Working for the bookstore Practice 17:
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a) What are the units of the residuals?
b) Which residual contributes the nigh to the sum that was minimized according to the Least Squares Benchmark to find this regression?
c) Which residual contributes to the lowest degree to that sum?
Sophie K.
Numerade Educator
Problem xx
Disk drives once more Hither are the residuals for a regression of Price on Capacity for the hard drives of Exercise 18.
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a) Which balance contributes the most to the sum that is minimized past the Least Squares criterion?
b) Two of the residuals are negative. What does that mean most those drives? Exist specific and utilise the right units.
Trouble 21
Bookstore sales last time For the regression model for the bookstore of Exercise $17,$ what is the value of $R^{two}$ and what does it mean?
Sophie Grand.
Numerade Educator
Problem 22
Deejay drives encore For the difficult drive data of Exercise $18,$ interpret the value of $R^{2}$
Sophie Thou.
Numerade Educator
Trouble 23
Remainder plots Here are residual plots (residuals plotted against predicted values) for three linear regression models. Indicate which condition appears to be violated (linearity, outlier or equal spread) in each case.
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Sophie Grand.
Numerade Educator
Problem 24
Disk drives last fourth dimension Hither is a besprinkle plot of the residuals from the regression of the hard drive prices on their sizes from Exercise $xviii .$
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a) Are whatever assumptions or conditions violated? If so, which ones?
b) What would you lot recommend well-nigh this regression?
Trouble 25
Real estate A random sample of records of sales of homes from Feb xv to April $xxx,1993,$ from the files maintained by the Albuquerque Board of Realtors gives "the Toll and Size (in foursquare anxiety) of 117 homes. A regression to predict Price (in thousands of dollars) from Size has an $R$ -squared of $71.4 \% .$ The residuals plot indicated that a linear model is appropriate.
a) What are the variables and units in this regression?
b) What units does the slope have? 1 recollect the gradient is positive or peg
c) Do yous think the slope is positive or negative? Fxnlain
Problem 26
Roller coaster The Mitch Bell-ringer poll ranked the Tiptop 10 steel roller coasters in $2011 .$ A table in the previous chapter'southward exercises shows the length of the initial driblet (in feet) and the duration of the ride (in seconds). A regression to predict Duration from Drop has $R^{2}=15.2 \%$
a) What are the variables and units in this regression?
b) What units does the slope accept?
c) Practise you lot remember the slope is positive or negative? Explain.
Trouble 27
Existent manor again The regression of Price on Size of homes in Albuquerque had $R^{2}=71.4 \%,$ equally described in Exercise $25 .$ Write a sentence (in context, of course) summarizing what the $R^{ii}$ says nigh this regression.
Sophie K.
Numerade Educator
Problem 28
Coasters again Practice 26 examined the clan betwixt the Duration of a roller coaster ride and the height of its initial Drib, reporting that $R^{2}=15.2 \% .$ Write a sentence (in context, of form) summarizing what the $R^{two}$ says about this regression.
Sophie K.
Numerade Educator
Problem 29
Existent estate redux The regression of Price on Size of homes in Albuquerque had $R^{2}=71.4 \%,$ as described in Exercise 25
a) What is the correlation betwixt $\operator name{Size}$ and Toll? Explain why yous chose the sign $(+\text { or }-$ ) you lot did.
b) What would you predict about the Cost of a habitation one standard difference in a higher place average in Size?
c) What would you predict about the Price of a abode 2 standard deviations beneath boilerplate in Size?
Problem thirty
Another ride The regression of Duration of a roller coaster ride on the height of its initial $D$rop, described in Practice $26,$ had $R^{2}=15.2 \%$
a) What is the correlation between $D$rop and Elapsing?
b) What would y'all predict about the Duration of the ride on a coaster whose initial Drib was 1 standard divergence below the mean Driblet?
c) What would y'all predict about the Duration of the ride on a coaster whose initial Driblet was 3 standard deviations in a higher place the mean Driblet?
Sophie K.
Numerade Educator
Problem 31
More real estate Consider the Albuquerque home sales from Do 25 again. The regression analysis gives the model Price $=47.82+0.061$ Size.
a) Explain what the slope of the line says near housing prices and house size.
b) What price would y'all predict for a 3000 -square-foot house in this market?
c) A real estate amanuensis shows a potential buyer a 1200 -square-pes dwelling, proverb that the asking toll is $\$ 6000$ less than what one would await to pay for a house of this size. What is the request price, and what is the $\$ 6000$ called?
Trouble 32
Final ride Consider the roller coasters described in Do 26 over again. The regression analysis gives the model Elapsing $=64.232+0.180$ Driblet.
a) Explain what the slope of the line says well-nigh how long a roller coaster ride may last and the height of the coaster.
b) A new roller coaster advertises an initial drop of 200 feet. How long would you predict the rides terminal?
c) Another coaster with a 150 -human foot initial drop advertises a 2-minute ride. Is this longer or shorter than you'd look? Past how much? What's that chosen?
Problem 33
Misinterpretations A Biological science student who created a regression model to utilize a bird's Pinnacle when perched for predicting its Wingspan fabricated these two statements. Assuming the calculations were washed correctly, explain what is wrong with each interpretation.
a) My $R^{2}$ of $93 \%$ shows that this linear model is appropriate.
b) A bird x inches alpine will take a wingspan of 17 inches.
Problem 34
More misinterpretations A Sociology student investigated the association between a country's Literacy Rate and Life Expectancy, so drew the conclusions listed below. Explain why each argument is incorrect. (Assume that all the calculations were done properly.)
a) The Literacy Rate determines $64 \%$ of the Life Expectancy for a country.
b) The slope of the line shows that an increase of $5 \%$ in Literacy Rate will produce a 2 -year improvement in Life Expectancy.
Problem 35
ESP People who merits to "take ESP" participate in a screening examination in which they have to gauge which of several images someone is thinking of. You and a friend both took the test. Yous scored ii standard deviations above the hateful, and your friend scored i standard departure beneath the hateful. The researchers offer anybody the opportunity to take a retest.
a) Should you choose to take this retest? Explain.
b) At present explain to your friend what his decision should be and why.
Sophie K.
Numerade Educator
Problem 36
SI jinx Players in any sport who are having great seasons, turning in performances that are much better than anyone might take predictable, oftentimes are pictured on the cover of Sports Illustrated. Often, their performances then falter somewhat, leading some athletes to believe in a "Sports Illustrated jinx." Similarly, it is mutual for astounding rookies to have less stellar second seasons - the so-called "sophomore slump." While fans, athletes, and analysts have proposed many theories about what leads to such declines, a statistician might offer a simpler (statistical) caption. Explicate.
Problem 37
Cigarettes Is the nicotine content of a cigarette related to the "tars"? A collection of data (in milligrams) on 29 cigarettes produced the scatterplot, residuals plot, and regression assay shown:
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Problem 38
Attendance 2010 In the previous affiliate, you looked at the relationship between the number of wins by Americar League baseball teams and the boilerplate attendance at their dwelling games for the 2010 season. Hither are the scatterplot, the residuals plot, and part of the regression assay:
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a) Do y'all recall a linear model is appropriate here? Explicate.
b) Interpret the pregnant of $R^{2}$ in this context.
c) Do the residuals show any pattern worth remarking on?
d) The betoken in the upper correct of the plots is the New York Yankees. What can you say about the residual for the Yanl
Problem 39
Another cigarette Consider again the regression of Nicotine content on Tar (both in milligrams) for the cigarettes examined in Practise 37
a) What is the correlation between Tar and Nicotine?
b) What would you predict about the average Nicotine content of cigarettes that are 2 standard deviations below average in Tar content?
c) If a cigarette is 1 standard deviation above boilerplate in Nicotine content, what do y'all suspect is true about its Tar content?
Sophie K.
Numerade Educator
Problem 40
Second inning 2010 Consider again the regression of $A v$ average Attendance on Wins for the baseball teams examined in Exercise 38
a) What is the correlation between Wins and Average Omnipresence?
b) What would you predict virtually the Boilerplate Omnipresence for a team that is 2 standard deviations above average in Wins?
c) If a team is 1 standard deviation below average in attendance, what would you predict virtually the number of games the team has won?
Problem 41
Last cigarette Take another look at the regression analysis of tar and nicotine content of the cigarettes in Practise 37
a) Write the equation of the regression line.
b) Estimate the Nicotine content of cigarettes with
4 milligrams of Tar.
c) Interpret the significant of the gradient of the regression line in this context.
d) What does the $y$ -intercept hateful?
e) If a new brand of cigarette contains 7 milligrams of tar and a nicotine level whose residual is $-0.5 \mathrm{mg},$ what is the nicotine content?
Problem 43
Income and housing revisited In Chapter $6,$ Do $32,$ we learned that the Office of Federal Housing Enterprise Oversight (OFHEO) collects data on diverse aspects of housing costs around the Usa. Hither'due south a scatterplot (by state) of the Housing cost Index (HCI) versus the Median Family unit Income (MFI) for the 50 states. The correlation is $r=0.65 .$ The mean HCI is 338.ii with a standard deviation of $116.55 .$ The mean MFI is $\$ 46,234,$ with a standard departure of $\$ 7072.47$.
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a) Is a regression analysis appropriate? Explain.
b) What is the equation that predicts Housing cost Index from median family income?
c) For a country with $\mathrm{MFI}=\$ 44,993, what would be the predicted HCI?
d) Washington, DC, has an MFI of $\$ 44,993 and an HCI
of $548.02 .$ How far off is the prediction in c) from the actual HCI?
e) If we standardized both variables, what would be the regression equation that predicts standardized HCI from standardized MFI?
f) If we standardized both variables, what would be the regression equation that predicts standardized MFI from standardized HCI?
Trouble 44
Interest rates and mortgages once more In Chapter 6 Exercise $33,$ we saw a plot of mortgages in the United States (in thousands of dollars) versus the interest rate at various times over the past 26 years. The correlation is $r=-0.86 .$ The hateful mortgage corporeality is $\$ 121.8 thousand and the mean interest rate is $7.74 \% .$ The standard deviations are $\ 47.36$ chiliad for mortgage amounts and i.79 \% for the involvement rates.
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a) Is a regression model advisable for predicting mortgage corporeality from interest rates? Explain.
b) What is the equation that predicts mortgage amount from interest rates?
c) What would you predict the mortgage amount would exist if the interest rates climbed to $13 \% ?
d) Do yous have any reservations about your prediction in part c)?
e) If we standardized both variables, what would exist the regression equation that predicts standardized mortgage amount from standardized involvement rates?
f) If we standardized both variables, what would be the regression equation that predicts standardized interest rates from standardized mortgage amount?
Problem 45
Online clothes An online wear retailer keeps rails of its customers' purchases. For those customers who signed up for the visitor'due south credit card, the company besides has information on the customer'south $A 1000 e$ and Income. A random sample of 500 of these customers shows the following scatterplot of Total Yearly Purchases past Age:
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a) What is the linear regression equation for predicting Total Yearly Purchase from Age?
b) Practice the assumptions and conditions for regression announced to exist met?
c) What is the predicted average Total Yearly Purchase for an 18 -year-former? For a 50 -twelvemonth-old?
d) What percent of the variability in Total Yearly Purchases is deemed for by this model?
e) Practise you retrieve the regression might be a useful one for the visitor? Explain.
Problem 46
Online dress II For the online clothing retailer discussed in the previous trouble, the scatterplot of Total Yearly Purchases by Income shows
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a) What is the linear regression equation for predicting Total Yearly Buy from Income?
b) Exercise the assumptions and conditions for regression appear to exist met?
c) What is the predicted boilerplate Full Yearly Purchase for someone with a yearly Income of 20,000 ? For someone with an annual Income of $\$ eighty,000 ?
d) What percent of the variability in Full Yearly Purchases is accounted for by this model?
e) Do yous think the regression might be a useful one for the company? Comment.
Problem 47
Sat scores The Sat is a test oftentimes used as function of an application to college. SAT scores are between 200 and $800,$ just accept no units. Tests are given in both Math and Verbal areas. Doing the SAT-Math problems also involves the ability to read and empathise the questions, just can a person's exact score be used to predict the math score? Exact and math SAT scores of a loftier school graduating grade are displayed in the scatterplot, with the regression line added.
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a) Describe the relationship.
b) Are there any students whose scores practise not seem to fit the overall pattern?
c) Notice the correlation coefficient and translate this value in context.
d) Write the equation of the regression line, defining any variables used in the equation.
e) Translate the gradient of this line.
f) Predict the math score of a student with a verbal score of 500
g) Every twelvemonth some student scores a perfect 1600 on these two parts of the test. Based on this model, what would be that pupil's Math score residual?
Problem 48
Success in college Colleges use Saturday scores in the admissions process because they believe these scores provide some insight into how a high schoolhouse educatee will perform at the college level. Regression analysis was computed on using $S A T$ to predict $G P A$.
(FIGURE CANNOT COPY)
a) Write the equation of the regression line.
b) Explicate what the $y$ -intercept of the regression line indicates.
c) Interpret the gradient of the regression line.
d) Predict the GPA of a freshman who scored a combined 2100
e) Based upon these statistics, how effective do you call up Sabbatum scores would be in predicting academic success during the first semester of the freshman year at this college? Explain.
f) As a pupil, would yous rather have a positive or a negative residual in this context? Explicate.
Problem 49
SAT, take 2 Suppose the AP calculus students complained and insisted that we should use Saturday math scores to judge verbal scores (using the same information from do 47 ). Hither is the regression analysis of Math $S A T$ vs. Verbal $South A T$
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a) What is the correlation?
b) Write the equation of the line of regression predicting verbal scores from math scores.
c) In general, what would a positive residual mean in this context?
d) A person tells you her math score was $500 .$ Predict her verbal score.
e) Using that predicted verbal score and the equation you created in Practice $47,$ predict her math score.
f) Why doesn't the upshot in part e) come out to $500 ?$
Problem 50
Success, part 2 The standard difference of the residuals
Trouble 51
Wildfires 2010 The National Interagency Burn Center (www.nifc.gov) reports statistics about wildfires. Here'southward an analysis of the number of wildfires between 1985 and 2010 .
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a) Is a linear model appropriate for these data? Explicate.
b) Interpret the slope in this context.
c) Can nosotros interpret the intercept? Why or why not?
d) What does the value of $s_{e}$ say about the size of the residuals? What does information technology say most the effectiveness of the model?
e) What does $R^{two}$ mean in this context?
Problem 52
Wildfires $2010-$ sizes We saw in Exercise 51 that the number of fires was nearly constant. But has the damage they cause remained abiding too? Here's a regression that examines the tendency in Acres per Fire, (in hundreds of thousands of acres) together with some supporting plots:
(FIGURE CANNOT COPY)
a) Is the regression model appropriate for these data? Explain.
b) What interpretation (if whatsoever) tin can you give for the $R^{2}$ in the regression tabular array?
Trouble 53
Used cars 2011 Carmax.com lists numerous Toyota Corollas for sale within a 250 mile radius of Redlands, CA. The table below shows the ages of the cars and the advertised prices.
a) Make a scatterplot for these data.
b) Describe the association between $A g e$ and Price of a used Corolla.
c) Do you think a linear model is appropriate?
d) Computer software says that $R^{ii}=89.1 \% .$ What is the correlation between $A thousand due east$ and Price$?$
due east) Explain the significant of $R^{ii}$ in this context.
f) Why doesn't this model explain $100 \%$ of the variability in the price of a used Corolla?
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Trouble 54
Drug abuse In the exercises of the last chapter you examined results of a survey conducted in the United states and x countries of Western Europe to determine the percentage of teenagers who had used marijuana and other drugs. Below is the scatterplot. Summary statistics showed that the mean percent that had used marijuana was $23.9 \%$ with a standard difference of $15.half dozen \% .$ An average of $11.six \%$ of teens had used other drugs, with a standard deviation of $10.two \%$
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Problem 55
More used cars 2011 Employ the advertised prices for Toyota Corollas given in Exercise 53 to create a linear model for the relationship between a car'south $A one thousand due east$ and its Price.
a) Observe the equation of the regression line.
b) Explicate the meaning of the slope of the line.
c) Explain the meaning of the $y$ -intercept of the line.
d) If you want to sell a 7 -yr-onetime Corolla, what price seems appropriate?
due east) Y'all have a chance to buy one of two cars. They are about the same age and appear to be in every bit good status. Would you rather buy the one with a positive residue or the one with a negative rest? Explicate.
f) Y'all see a "For Sale" sign on a 10-year-old Corolla stating the request cost as $\$ 8,500 .$ What is the residual?
g) Would this regression model exist useful in establishing a off-white price for a 25 -year-old car? Explain.
Trouble 56
Birthrates 2009 The table shows the number of alive births per 1000 women aged $fifteen-44$ years in the United States, starting in $1965 .$ (National Center for Health Statistics, www.cdc.gov/nchs/)
(GRAPHS CANNOT COPY)
a) Brand a scatterplot and describe the general trend in Birthrates. (Enter Year as years since $1900: 65,lxx,75,$ etc.)
b) Detect the equation of the regression line.
c) Check to run across if the line is an appropriate model. Explain.
d) Interpret the gradient of the line.
e) The table gives rates only at 5 -year intervals. Estimate what the charge per unit was in $1978 .$
f) In $1978,$ the birthrate was actually $15.0 .$ How close did your model come?
g) Predict what the Birthrate will be in $2010 .$ Comment on your faith in this prediction.
h) Predict the Birthrate for $2025 .$ Comment on your faith
Problem 57
Burgers In the last chapter, you examined the association between the amounts of Fatty and Calories in fast-food hamburgers. Here are the data:
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a) Create a scatterplot of Calories vs. Fatty.
b) Interpret the value of $R^{2}$ in this context.
c) Write the equation of the line of regression.
d) Utilize the residuals plot to explain whether your linear model is advisable.
e) Explain the meaning of the $y$ -intercept of the line.
f) Explicate the pregnant of the gradient of the line.
one thousand) A new burger containing 28 grams of fatty is introduced. According to this model, its residual for calories is $+33 .$ How many calories does the burger take?
Problem 58
Chicken Chicken sandwiches are often advertised equally a healthier alternative to beefiness because many are lower in fat. Data from tests on 15 different sandwiches randomly selected from the website http:// fast-food-nutrition. findthebest.com/d/a/ChickenSandwich produced the Calories vs. Fat scatterplot and the regression analysis below.
a) Practice you think a linear model is appropriate in this state of affairs?
b) Describe the forcefulness of this association.
c) Write the equation of the regression line to estimate calories from the fat content.
d) Explicate the meaning of the slope.
due east) Explain the meaning of the $y$ -intercept.
f) What does it hateful if a certain sandwich has a negative rest?
Problem 59
A 2d helping of burgers In Exercise 57 yous created a model that can guess the number of Calories in a burger when the Fat content is known.
a) Explain why y'all cannot use that model to estimate the fat content of a burger with 600 calories.
b) Make that estimate using an appropriate model.
Sophie K.
Numerade Educator
Problem 60
A second helping of craven In Exercise 58 yous created a model to estimate the number of Calories in a craven sandwich when you know the Fatty.
a) Explain why you cannot utilize that model to estimate the fat content of a 400 -calorie sandwich.
b) Quiznos big mesquite sandwich stands out on the graph with an impressive 53 fat grams and 1 190 calories. What effect practice y'all call up this value has on the regression equation?
Problem 61
Body fat It is difficult to determine a person's body fatty percentage accurately without immersing him or her in water. Researchers hoping to notice ways to brand a practiced estimate immersed 20 male subjects, then measured their waists and recorded their weights.
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a) Create a model to predict \%Body Fatty from Weight.
b) Exercise you think a linear model is appropriate? Explain.
c) Interpret the slope of your model.
d) Is your model likely to make reliable estimates? Explicate.
c) What is the balance for a person who weighs 190
Problem 62
Trunk fatty again Would a model that uses the person'south Waist size be able to predict the $\%$ Torso Fat more accurately than one that uses Weight? Using the information in Practise $61,$ create and analyze that model.
Problem 63
Heptathlon 2004 Nosotros discussed the women'south Olympic heptathlon in Chapter $five .$ The table shows the results from the high jump, 800 -meter run, and long jump fo the 26 women who successfully completed all three events in the 2004 Olympics.
(GRAPHS CANNOT COPY)
Let's examine the association among these events. Perform a regression to predict high-jump performance from the 800-meter results.
a) What is the regression equation? What does the slope mean?
b) What per centum of the variability in high jumps tin be deemed for by differences in $800-\mathrm{grand}$ times?
c) Do good loftier jumpers tend to be fast runners? (Be conscientious - low times are adept for running events and high distances are adept for jumps.)
d) What does the residuals plot reveal well-nigh the model?
e) Do you retrieve this is a useful model? Would you employ information technology to predict loftier-leap performance? (Compare the residual standard deviation to the standard deviation of the high jumps.)
Trouble 64
Heptathlon 2004 again We saw the information for the women's 2004 Olympic heptathlon in Exercise $63 .$ Are the ii jumping events associated? Perform a regression of the long-leap results on the loftier-bound results.
a) What is the regression equation? What does the gradient mean?
b) What percentage of the variability in long jumps can be accounted for by high-jump performances?
c) Practice proficient high jumpers tend to be good long jumpers?
d) What does the residuals plot reveal most the model?
due east) Do you remember this is a useful model? Would you lot apply it to predict long-jump performance? (Compare the remainder standard deviation to the standard divergence of the long jumps.)
Trouble 65
Least squares I Consider the iv points $(10,10),(20,$ 50), (twoscore, 20), and (50,80). The least squares line is $\chapeau{y}=7.0+one.one x .$ Explain what "to the lowest degree squares" means, using these data as a specific instance.
Trouble 66
Least squares 2 Consider the four points (200,1950) $(400,1650),(600,1800),$ and $(800,1600) .$ The least squares line is $\hat{y}=1975-0.45 10 .$ Explicate what "least squares" means, using these data as a specific instance.
Sophie K.
Numerade Educator
Source: https://www.numerade.com/books/chapter/linear-regression-2/
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