Simple Linear RegressionMultiple Linear RegressionOther Considerations in the Regression ModelTextbook Theory Questions 3.7 Exercises Describe the null hypotheses to which the p-values given in Table…

Simple Linear RegressionMultiple Linear RegressionOther Considerations in the Regression ModelTextbook Theory Questions 3.7 Exercises

Describe the null hypotheses to which the p-values given in Table 3.4 correspond. Explain what conclusions you can draw based on these p-values. Your explanation should be phrased in terms of sales, TV, radio, and newspaper, rather than in terms of the coefficients of the linear model.

Q3 Applied Textbook Questions with Python 3.7 Exercises

Hint – several github sites have the complete solution in python e.g.

This question involves the use of simple linear regression on the Auto data set. (a) Perform a simple linear regression with mpg as the response and horsepower as the predictor. Print the results. Comment on the output. For example:

i. Is there a relationship between the predictor and the response?

ii. How strong is the relationship between the predictor and the response?

iii. Is the relationship between the predictor and the response positive or negative?

iv. Predictions

What is the predicted mpg associated with a horsepower of 98? What are the associated 95 % confidence and prediction intervals?Plot the response and the predictor, display the least squares regression line.Produce diagnostic plots of the least squares regression fit. Comment on any problems you see with the fit.This question involves the use of multiple linear regression on the Auto data set.

(a) Produce a scatterplot matrix which includes all of the variables in the data set.

(b) Compute the matrix of correlations between the variables.

(c) Perform a multiple linear regression with mpg as the response and all other variables except name as the predictors and print the results. Comment on the output. For instance:

i. Is there a relationship between the predictors and the response?

ii. Which predictors appear to have a statistically significant relationship to the response?

iii. What does the coefficient for the year variable suggest?

(d) Produce diagnostic plots of the linear regression fit. Comment on any problems you see with the fit. Do the residual plots suggest any unusually large outliers? Does the leverage plot identify any observations with unusually high leverage?

(e) Fit linear regression models with interaction effects. Do any interactions appear to be statistically significant?

(f) Try a few different transformations of the variables, such as log(X), √ X, X2. Comment on your findings.


This problem involves the Boston data set, which we saw in the lab for this chapter. We will now try to predict per capita crime rate using the other variables in this data set. In other words, per capita crime rate is the response, and the other variables are the predictors.

(a) For each predictor, fit a simple linear regression model to predict the response. Describe your results. In which of the models is there a statistically significant association between the predictor and the response? Create some plots to back up your assertions.

(b) Fit a multiple regression model to predict the response using all of the predictors. Describe your results. For which predictors can we reject the null hypothesis H0 : βj = 0?

(c) How do your results from (a) compare to your results from (b)? Create a plot displaying the univariate regression coefficients from (a) on the x-axis, and the multiple regression coefficients from (b) on the y-axis. That is, each predictor is displayed as a single point in the plot. Its coefficient in a simple linear regression model is shown on the x-axis, and its coefficient estimate in the multiple linear regression model is shown on the y-axis.

(d) Is there evidence of a non-linear association between any of the predictors and the response? To answer this question, for each predictor X, fit a model of the form Y = β0 + β1X + β2X2 + β3X3 + .

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Sample Solution
The United States is home to probably the most famous and productive sequential executioners ever. Names, for example, Ted Bundy, Gary Ridgeway, and the Zodiac Killer have become commonly recognized names because of the awful idea of their violations. One of the most productive sequential executioners in American history is John Wayne Gacy. Nicknamed the Killer Clown in view of his calling, Gacy assaulted and killed at any rate 33 adolescent young men and youngsters somewhere in the range of 1972 and 1978, which is one of the most noteworthy realized unfortunate casualty checks. Gacy’s story has become so outstanding that his wrongdoings have been highlighted in mainstream society and TV appears, for example, American Horror Story: Hotel and Criminal Minds. Scientific science has, and keeps on playing, a significant job in the understanding of the case and distinguishing proof of the people in question. John Wayne Gacy’s history of sexual and psychological mistreatment was instrumental in arousing examiner’s curiosity of him as a suspect. John Wayne Gacy was conceived on March 17, 1942, in Chicago, Illinois. Being the main child out of three kids, Gacy had a stressed association with his dad, who drank intensely and was frequently injurious towards the whole family (Sullivan and Maiken 48). In 1949, a temporary worker, who was a family companion, would pet Gacy during rides in his truck; notwithstanding, Gacy never uncovered these experiences to his folks inspired by a paranoid fear of reprisal from his dad (Foreman 54). His dad’s mental maltreatment proceeded into his young grown-up years, and Gacy moved to Las Vegas where he worked quickly in the emergency vehicle administration before turning into a funeral home chaperon (Sullivan and Maiken 50). As a funeral home orderly, Gacy was vigorously associated with the preserving procedure and conceded that one night, he moved into the casket of an expired adolescent kid and touched the body (Cahill and Ewing 46). Stunned at himself, Gacy comes back to Chicago to live with his family and graduates from Northwestern Business College in 1963, and acknowledges an administration learner position with Nunn-Bush Shoe Company. In 1964, Gacy is moved to Springfield and meets his future spouse, Marlynn Myers. In Springfield, Gacy has his subsequent gay experience when an associate shakily performed oral sex on him (London 11:7). Gacy moves to Waterloo, Iowa, and starts a family with Myers. Be that as it may, after consistently undermining his better half with whores, Gacy submits his originally known rape in 1967 upon Donald Vorhees. In the coming months, Gacy explicitly manhandles a few different adolescents and is captured and accused of oral homosexuality (Sullivan and Maiken 60). On December 3, 1968, Gacy is indicted and condemned to ten years at the Anamosa State Penitentiary. Gacy turns into a model detainee at Anamosa and is conceded parole in June of 1970, a unimportant year and a half after his condemning. He had to move to Chicago and live with his mom and watch a 10:00PM time limitation. Not exactly a year later, Gacy is accused again of explicitly ambushing an adolescent kid however the young didn’t show up in court, so the charges were dropped. Gacy was known by numerous individuals in his locale to be an eager volunteer and being dynamic in network governmental issues. His job as “Pogo the Clown” the comedian started in 1975 when Gacy joined a nearby “Jaunty Joker” jokester club that consistently performed at raising money occasions. On January 3, 1972, Gacy submits his first homicide of Timothy McCoy, a 16-year old kid heading out from Michigan to Omaha. Guaranteeing that McCoy went into his room employing a kitchen blade, Gacy gets into a physical fight with McCoy before wounding him over and over in the chest. In the wake of understanding that McCoy had absentmindedly strolled into the stay with the blade while attempting to get ready breakfast, Gacy covers the body in his slither space. Gacy conceded in the meetings following his capture that executing McCoy gave him a “mind-desensitizing climax”, expressing that this homicide was the point at which he “understood passing was a definitive rush” (Cahill and Ewing 349). Very nearly 2 years after the fact, Gacy submits his second homicide of a unidentified young person. Gacy choked the kid before stuffing the body in his wardrobe before covering him (Cahill 349). In 1975, Gacy’s business was developing rapidly and his craving for youngsters developed with it. Gacy regularly tricked youngsters under his work to his home, persuading them to place themselves in cuffs, and assaulting and tormenting them before choking them (Cahill 169-170). The greater part of Gacy’s killings occurred somewhere in the range of 1976 and 1978, the first of this time occurring in April 1976. Huge numbers of the young people that were killed during this time were covered in a slither space under Gacy’s home. For the rest of the homicides, Gacy confessed to losing five bodies the I-55 scaffold into the Des Plaines River; be that as it may, just four of the bodies were ever recouped (Linedecker 152). In December 1978, Gacy meets Robert Jerome Piest, a 15-year old kid working at a drug store and extends to him an employment opportunity at Gacy’s firm. Piest illuminates his mom regarding this and neglects to restore that night. The Piest family documents a missing individual’s report and the drug specialist educates police that Gacy would no doubt be the man that Jerome addressed about a vocation. When addressed by the police, Gacy denied any inclusion in Piest’s vanishing. In any case, the police were not persuaded, and Gacy’s history of sexual maltreatment and battery incited the police to look through his home. Among the things found at Gacy’s home were a 1975 secondary school class ring with the initials J.A.S., numerous driver’s licenses, cuffs, attire that was unreasonably little for Gacy, and a receipt for the drug store that Piest had worked at. Throughout the following scarcely any days, specialists got various calls and tips about Gacy’s rapes and the strange vanishings of Gacy’s representatives. The class ring was in the end followed back to John A. Szyc, one of Gacy’s exploited people in 1977. Futhermore, after inspecting Gacy’s vehicle, specialists found a little bunch of filaments looking like human hair, which were sent to the labs for additional investigation. That equivalent night, search hounds were utilized to identify any hint of Piest in Gacy’s vehicle, and one of the mutts showed that Piest had, truth be told, been available in the vehicle. On December 20, 1977, under the pressure of steady police observation and examination, Gacy admits to more than 30 homicides and educates his legal counselor and companion where the bodies were covered, both in the slither space and the stream. 26 exploited people were found in the slither space and 4 in the waterway. Gacy is captured, indicted for 33 killings, and condemned to death by deadly infusion. He endeavored a craziness supplication yet was denied, and was executed on May 10, 1994. There were a few measurable pointers that specialists used to attach Gacy to the homicides. A portion of these include fiber investigation, dental and radiology records, utilizing the deterioration procedure of the human body, and facial reproduction in recognizing the people in question. Examiners discovered strands that looked like human hair in both Gacy’s vehicle and close to the creep space where the bodies were covered. Notwithstanding these hair tests, specialists likewise discovered filaments that contained hints of Gacy’s blood and semen in a similar region. Blood having a place with the unfortunate casualties was found on a portion of the strands, which would later legitimately attach Gacy to the violations. The filaments in Gacy’s vehicle were broke down by scientific researchers and coordinated Piest’s hair tests. Besides, the pursuit hounds that confirmed that Piest had been in Gacy’s vehicle showed this by a “demise response”, which told specialists that Piest’s dead body had been within Gacy’s vehicle. Out of Gacy’s 33 known unfortunate casualties, just 25 were ever convincingly distinguished. A large number of Gacy’s unfortunate casualties had comparative physical depictions and were subsequently difficult to distinguish by absolutely asking people in general. To distinguish the people in question, examiners went to Betty Pat Gatliff, a pioneer in scientific science and facial recreation. Facial remaking is the way toward reproducing the facial highlights of a person by utilizing their remaining parts. Certain facial highlights, for example, facial structures, nasal structure, and in general face shape can be valuable in distinguishing an unfortunate casualty even long in the afterlife. By utilizing these highlights, and with the assistance of program, scientific examiners can make a picture of an individual’s face, which is instrumental in distinguishing unfortunate casualties after their bodies have rotted. Facial reproduction should be possible in a few measurements. Two-dimensional facial recreations is utilized with skull radiographs and depend on pre-passing photos and data. In any case, this isn’t really perfect on the grounds that cranial highlights are not constantly obvious or at the correct scale (Downing). So as to get a reasonable and increasingly precise portrayal of the unfortunate casualty’s face, a craftsman and a scientific anthropologist are normally essential (Downing). Three-dimensional facial remaking is finished by figures or high goals, three-dimensional pictures. PC programs can make facial reproductions by controlling examined photos of the remaining parts and use approximations to reproduce facial highlights. These will in general produce results that don’t look counterfeit (Reichs and Craig 491). Once in a while, examiners will utilize a strategy called superimposition as a procedure for facial remaking. Tragically, it’s anything but a usually utilized strategy, as it expects specialists to have some information about the character of the remaining parts they are managing. By superimposing a photo of a person over the skeletal remains, agents can check whether the facial highlights line up with the anatomical highlights, permitting them to distinguish an unfortunate casualty. On account of John Wayne Gacy’s exploited people, specialists had the option to utilize facial remaking to distinguish nine of the bodies found in the slither space. The accompanying realistic shows the facial reproductions of these nine exploited people: Since facial recreation was insufficient to distinguish the entirety of the v>GET ANSWER Let’s block ads! (Why?)

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