Discuss any of the following topics from the text book
“ISLR” An Introduction to Statistical Learning, Gareth James, Daniela Witten, Trevor Hastie and Robert Tibshirani, http://www-bcf.usc.edu/~gareth/ISL/index.html
3 Linear Regression 59
3.1 Simple Linear Regression . . . . . . . . . . . . . . . . . . . 61
3.1.1 Estimating the Coefficients . . . . . . . . . . . . . . 61
3.1.2 Assessing the Accuracy of the Coefficient Estimates . . . . . . . . . . . . . . . . . . . . . . . . 63
3.1.3 Assessing the Accuracy of the Model . . . . . . . . . 68
3.2 Multiple Linear Regression . . . . . . . . . . . . . . . . . . 71
3.2.1 Estimating the Regression Coefficients . . . . . . . . 72
3.2.2 Some Important Questions . . . . . . . . . . . . . . 75
3.3 Other Considerations in the Regression Model . . . . . . . . 82
3.3.1 Qualitative Predictors . . . . . . . . . . . . . . . . . 82
3.3.2 Extensions of the Linear Model . . . . . . . . . . . . 86
3.3.3 Potential Problems . . . . . . . . . . . . . . . . . . . 92
3.4 The Marketing Plan . . . . . . . . . . . . . . . . . . . . . . 102
3.5 Comparison of Linear Regression with K-Nearest Neighbors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5
words : 250
and also provide replies to below 3 student posts each in 150 words,
chaitanya- One very important question is how the variables are related. For example, we could ask for the relationship between peopleâs weights and heights, or study time and test scores, or two animal populations. Regression is a set of techniques for estimating relationships, and weâll focus on them for the next two chapters. In this chapter, weâll focus on finding one of the simplest type of relationship: linear. This process is unsurprisingly called linear regression, and it has many applications. For example, we can relate the force for stretching a spring and the distance that the spring stretches or explain how many transistors the semiconductor industry can pack into a circuit over time. Despite its simplicity, linear regression is an incredibly powerful tool for analysing data. While weâll focus on the basics in this chapter, the next chapter will show how just a few small tweaks and extensions can enable more complex analyses
Linear regression is a simple approach to supervised learning. It assumes that the dependence of Y on X1, X2, . . .Xp is linear.Linear regression is a simple approach to supervised learning. It assumes that the dependence of Y on X1, X2, . . .Xp is linear. True regression functions are never linear.
By examining the second equation for the estimated slope Î²Ë 1, we see that since sample standard deviations sx and sy are positive quantities, the correlation coefficient r, which is always between â1 and 1, measures how much x is related to y and whether the trend is positive or negative. Figure 3.2 illustrates different correlation strengths. The square of the correlation coefficient r 2 will always be positive and is called the coefficient of determination. As weâll see later, this also is equal to the proportion of the total variability thatâs explained by a linear model. As an extremely crucial remark, correlation does not imply causation! We devote the entire next page to this point, which is one of the most common sources of error in interpreting statistics.
In particular, the residual is defined to be yi â yËi : the distance from the original data point to the predicted value on the line. You can think of it as the error left over after the model has done its work. This difference is shown graphically in Figure 3.5. Note that the residual yi â yË isnât quite the same as the noise ε! Weâll talk a little more about analyzing residuals (and why this distinction matters) in the next chapter. If our model is doing a good job, then it should explain most of the difference from ¯y, and the first term should be bigger than the second term. If the second term is much bigger, then the model is probably not as useful.
kranthi – inear regression is a technique used to model the relationships between observed variables. The idea behind simple linear regression is to “fit” the observations of two variables into a linear relationship between them (James et al. 2017). Graphically, the task is to draw the line that is “best-fitting” or “closest” to the points(xi,yi), where xi and yi are observations of the two variables which are expected to depend linearly on each other.
Regression is a common process used in many applications of statistics in the real world. There are two main types of applications:
Predictions: After a series of observations of variables, regression analysis gives a statistical model for the relationship between the variables (Seal, 1997). This model can be used to generate predictions: given two variables xx and y,y, the model can predict values of yy given future observations of x.x. This idea is used to predict variables in countless situations, e.g. the outcome of political elections, the behavior of the stock market, or the performance of a professional athlete.
Correlation: The model given by a regression analysis will often fit some kinds of data better than others. This can be used to analyze correlations between variables and to refine a statistical model to incorporate further inputs: if the model describes certain subsets of the data points very well, but is a poor predictor for other data points, it can be instructive to examine the differences between the different types of data points for a possible explanation. This type of application is common in scientific tests, e.g. of the effects of a proposed drug on the patients in a controlled study.
urmila – Regression analysis is a significant statistical method for the analysis of restorative information. It empowers the ID and portrayal of connections among numerous variables. It likewise empowers the ID of prognostically pertinent hazard factors and the figuring of hazard scores for singular prognostication. (Schneider, Hommel, & Blettner, 2010)
Regression analysis utilizes a model that portrays the connections between the dependent variables and the independent variables in a rearranged scientific structure. There might be natural motivations to expect from the earlier that a specific sort of scientific capacity will best depict such a relationship, or straightforward suppositions must be made this is the situation.
Linear regression is utilized to examine the linear connection between a dependent variable Y (circulatory strain) and at least one independent variable X (age, weight, sex). The dependent variable Y must be constant, while the independent variables might be either ceaseless (age), paired (sex), or absolute (economic wellbeing).
The underlying judgment of a potential connection between two constant variables ought to consistently be made based on a disperse plot (dissipate graph). Performing a linear regression bodes well just if the relationship is linear. Different methods must be utilized to examine nonlinear relationships. (Schneider, Hommel, & Blettner, 2010)
Univariable linear regression considers the linear connection between the dependent variable Y and a solitary independent variable X. The linear regression model depicts the dependent variable with a straight line that is characterized by the condition Y = a + b à X, where and is they-converge of the line, and b is its slant. (Schneider, Hommel, & Blettner, 2010)
Initially, the parameters an and b of the regression line are assessed from the estimations of the dependent variable Y and the independent variable X with the guide of statistical methods. The regression line empowers one to foresee the estimation of the dependent variable Y from that of the independent variable X. (Schneider, Hommel, & Blettner, 2010)
Sample Solution
This course was an extremely new encounter for me both from learning perspective and execution astute. The reasonable piece of the course was extremely useful where ones get an opportunity to actualize all the information gain during the talks and through self-considers. I have discovered that development requires cooperation, inventiveness, functional execution and enhanced the item. Also, this errand turns out to be a lot simpler on the off chance that you have an interdisciplinary group working for a bound together obje Xav-big data ctive. I have really taken in a foundational way to deal with planning an item, that how to begin without any preparation and nothing to assemble a client arranged or to bring another item into the market, how to work in groups for limited capacity to focus time, how to oversee and isolate undertakings inside the gathering, which venture the executives approach to apply contingent on the idea of the task, how to channel the necessities or prerequisites of the items, what to look like for licenses, benchmark for the specific undertaking you are taking a shot at to have the essential information on what as of now is out there accessible in the market. The most effective method to be innovative during the union of ideas for your theme or undertaking. In my learning journals I will clarify the ideas mastered during the talks, bunch works, workshops and generally through self-examines. I discovered that most significant piece of the arranging stage is building venture group. By and large attempt to build up your group as quickly as time permits. Distinguishing a couple of individuals in any event, during the underlying stages is additionally conceivable here and there. Designating the group early benefit from their possession to the venture, and boosts what they can contribute towards the item improvement. The initial phase in building a successful undertaking group is to make an asset plan. An asset plan expects you to comprehend and distinguish the work to be done and the human aptitudes required to finish it. An underlying arrangement is regularly a significant level layout and will be refined as you separate into parts the entire of your work. To build up a compelling group, you need to begin by picking the most ideally equipped individuals for the activity. This sounds self-evident, yet deciding t Xav-big data he best applicants isn’t constantly clear. Numerous elements concerning potential individuals must be considered, including variables, for example, the aptitudes expected of them to finish venture assignments, their degree of impact in the association, their entrance to a system of different assets, their ability to take an interest viably, their capacity to function admirably in a group situation. Once in a while, venture administrators don’t have the opportunity of picking colleagues. Individuals might be alloted to the venture group. In the event that this is your circumstance, it is imperative that you take additional consideration to set up an association with your colleagues before the group starts to meet as a gathering. Else, they may not feel associated with the remainder of the task group or, more regrettable, may feel put upon and come up short on any pledge to the venture. Correspondence is a basic piece of collaboration. Without fruitful correspondence, it is extremely hard to accomplish the ideal outcome. At the point when data is shared viably, the remaining task at hand is isolated between the colleagues and job needing to be done gets simpler for all. During our venture we utilized skype, whatsapp and Google drive for the correspondence purposes inside our gathering. With such a large number of accessible social applications nowadays in the market it’s extremely simpler for the groups to begin and have powerful correspondence right way. It is basic that group correspondence happens all through the venture so as to limit perplexity and pointless deferrals. Colleagues all the more unreservedly share their thoughts, contemplations and feelings, accordingly offering extra open doors for development and imagination. Messages to be imparted gotten rearranged when there is successful correspondence. Chances for errors are limited, if not through and through prohibited. Group consideration stays on the venture, finishing assignments and such exercises, and whatever vitality is vital to the greatest advantage of the undertaking. Source: http://www.brighthubpm.com/asset the board/ Figure 1. One out of five ventures is fruitless because of incapable interchanges. http://www.projecttimes.com/articles/powerful correspondence a-challenge-to-extend managers.html The item improvement procedure can be imagined as a channel with countless new item thoughts entering the idea organize, narrowing down to a less number in consequent stages. Isolating these each stage is a stage audit where a choice is made to skirt the item Xav-big data , go into the following stage or divert back to a past stage for e Xav-big data xtra work. The reason for the idea arrange is to rapidly survey another item openings. This movement will be performed by an item supervisor with help from others in the group. The item idea proposition will ordinarily include: depiction of item idea and one of a kind/new selling suggestion, Preliminary market opportunity appraisal, conservative diagram, specialized valuation, starter money related examination, arranged calendars, prescribed center colleagues. The goal of the framework level plan is to characterize the item which must be created, and to finish the business system for the item. During the following stage the suppositions made during the idea organize are confirmed through further statistical surveying and focused examination. Building suspicions will be confirmed in this phase by increasingly point by point plan and achievability tests. Figure 2 Product advancement process Source: https://sbpbusiness2000.wordpress.com/2013/01/25/new-item advancement/ Lean Startup item advancement urges us to initially explore if there is a need of the item in the market before we stress over the subtleties of the new item. While old-style approaches additionally suggest doing statistical surveying and concentrate before we take part in item arranging and definition, lean methodologies speed up at which a startup group will work. This permits startup groups to fall flat and adapt quicker, to adjust their item methodology and strategies quickly, and to ideally dispatch the correct item with the correct highlights in the market. Figure 3. Lean startup item advancement strategy Source: http://theleanstartup.com/standards We as a gathering picked lean and spry strategy for venture the executives. Lithe Software Development procedure is for a task that necessities out Xav-big data rageous spryness in prerequisites. Spry task the board centers around doing the procedure piece-by-piece, as opposed to in one major part like the conventional methodology. Nimble strategy handles venture change and intricacy through correspondence between venture colleagues and end clients. It empowers groups to suitably react to anomaly through short extra work areas, for example, Scrum ‘runs’. These dashes target bringing a well-tried, utilitarian working model. Arranging and changes in configuration happen all through the task dependent on exercises that are found out en route. There’s no disgrace in thinking back to refine the results or highlights of the item at any stage. The work nowadays are increasingly requesting and organizations need to create results of high caliber in a limited ability to focus time. The innovation is moving quickly and the business is globalizing where with the assistance of this innovation it’s simpler for littler and medium size organizations to arrive at the worldwide market. Then again the greater organizations are persistently improving their procedures, items and administrations are probably going to make due in the changing business sector where medium measured and new businesses are blasting at a quick speed. This is the reason the business has begun to enlist an ever increasing number of interdisciplinary groups for the item improvement. An interdisciplinary group comprises of pros of their own fields. A run of the mill interdisciplinary group incorporates experts of innovative work, building, fabricating, advertising, financial matters, expressions, business, and plan. By consolidating people’s qualities in a gathering will increase the value of the item and in the long run to the organization. Use of interdisciplinary groups has quickened the item improvement cycle which will result quick dispatch of the item into the market, brought down the generation costs as those groups will assess every single part of the item before sending it to the assembling stage, it is generally seen that time spend in innovative work stage before sending the item to assembling stage will diminish the expense of the item and stay away from pointless breaks, and even multiplied the evaluated deals. The estimation of interdisciplinary groups is that each part has their very own ability and perspective from their very own field. The assorted variety of the gathering builds access to various sorts of data. A gathering with the individuals all from various foundations can once in a while take care of the issues which will take a long time inside a week or even the issues which feel difficult to split. The gathering individuals likewise gain from one another and might get some significant contacts from different fields. Interestingly, every individual know their job in the gathering as per their own abilities set so they should contribute their greatest exertion. This lets them to concentrate on the parts they’re great at and different individuals will adjust them in the territories where they don’t have the center abilities. This will makes a positive climate and that expands efficiency. A group with various aptitude guarantees that every one of the undertakings of a task are finished. Much after this the interdisciplinary groups must have the ability, information, experience and specialized skill to take care of business. The group needs additionally a brought together objective and a decent pioneer who will lead them to the correct route during the time spent advancement. Collaboration is troublesome, particularly in a gathering with various aptitudes and ability. The gathering individuals may have contradicting perspectives which can prompt clashes, exercise in futility, and it>
This course was an extremely new encounter for me both from learning perspective and execution astute. The reasonable piece of the course was extremely useful where ones get an opportunity to actualize all the information gain during the talks and through self-considers. I have discovered that development requires cooperation, inventiveness, functional execution and enhanced the item. Also, this errand turns out to be a lot simpler on the off chance that you have an interdisciplinary group working for a bound together objective. I have really taken in a foundational way to deal with planning an item, that how to begin without any preparation and nothing to assemble a client arranged or to bring another item into the market, how to work in groups for limited capacity to focus time, how to oversee and isolate undertakings inside the gathering, which venture the executives approach to apply contingent on the idea of the task, how to channel the necessities or prerequisites of the items, what to look like for licenses, benchmark for the specific undertaking you are taking a shot at to have the essential information on what as of now is out there accessible in the market. The most effective method to be innovative during the union of ideas for your theme or undertaking. In my learning journals I will clarify the ideas mastered during the talks, bunch works, workshops and generally through self-examines. I discovered that most significant piece of the arranging stage is building venture group. By and large attempt to build up your group as quickly as time permits. Distinguishing a couple of individuals in any event, during the underlying stages is additionally conceivable here and there. Designating the group early benefit from their possession to the venture, and boosts what they can contribute towards the item improvement. The initial phase in building a successful undertaking group is to make an asset plan. An asset plan expects you to comprehend and distinguish the work to be done and the human aptitudes required to finish it. An underlying arrangement is regularly a significant level layout and will be refined as you separate into parts the entire of your work. Xav-big data To build up a compelling group, you need to begin by picking the most ideally equipped individuals for the activity. This sounds self-evident, yet deciding the best applicants isn’t constantly clear. Numerous elements concerning potential individuals must be considered, including variables, for example, the aptitudes expected of them to finish venture assignments, their degree of impact in the association, their entrance to a system of different assets, their ability to take an interest viably, their capacity to function admirably in a group situation. Once in a while, venture administrators don’t have the opportunity of picking colleagues. Individuals might be alloted to the venture group. In the event that this is your circumstance, it is imperative that you take additional consideration to set up an association with your colleagues before the group starts to meet as a gathering. Else, they may not feel associated with the remainder of the task group or, more regrettable, may feel put upon and come up short on any pledge to the venture. Correspondence is a basic piece of collaboration. Without fruitful correspondence, it is extremely hard to accomplish the ideal outcome. At the point when data is shared viably, the remaining task at hand is isolated between the colleagues and job needing to be done gets simpler for all. During our venture we utilized skype, whatsapp and Google drive for the correspondence purposes inside our gathering. With such a large number of accessible social applications nowadays in the market it’s extremely simpler for the groups to begin and have powerful correspondence right way. It is basic that group correspondence happens all through the venture so as to limit perplexity and pointless deferrals. Colleagues all the more unreservedly share their thoughts, contemplations and feelings, accordingly offering extra open doors for development and imagination. Messages to be imparted gotten rearranged when there is successful correspondence. Chances for errors are limited, if not through and through prohibited. Group consideration stays on the venture, finishing assignments and such exercises, and whatever vitality is vital to the greatest advantage of the undertaking. Source: http://www.brighthubpm.com/asset the board/ Figure 1. One out of five ventures is fruitless because of incapable interchanges. http://www.projecttimes.com/articles/powerful correspondence a-challenge-to-extend managers.html The item improvement procedure can be imagined as a channel with countless new item thoughts entering the idea organize, narrowing down to a less number in consequent stages. Isolating these each stage is a stage audit where a choice is made to skirt the item, go into the following stage or divert back to a past stage for extra work. The reason for the idea arrange is to rapidly survey another item openings. This movement will be performed by an item supervisor with help from others in the group. The item idea proposition will ordinarily include: depiction of item idea and one of a kind/new selling suggestion, Preliminary market opportunity appraisal, conservative diagram, speciali Xav-big data zed valuation, starter money related examination, arranged calendars, prescribed center colleagues. The goal of the framework level plan is to characterize the item which must be created, and to finish the business system for the item. During the following stage the suppositions made during the idea organize are confirmed through further statistical surveying and focused examination. Building suspicions will be confirmed in this phase by increasingly point by point plan and achievability tests. Figure 2 Product advancement process Source: https://sbpbusiness2000.wordpress.com/2013/01/25/new-item advancement/ Lean Startup item advancement urges us to initially explore if there is a need of the item in the market before we stress over the subtleties of the new item. While old-style approaches additionally suggest doing statistical surveying and concentrate before we take part in item arranging and definition, lean methodologies speed up at which a startup group will work. This permits startup groups to fall flat and adapt quicker, to adjust their item methodology and strategies quickly, and to ideally dispatch the correct item with the correct highlights in the market. Figure 3. Lean startup item advancement strategy Source: http://theleanstartup.com/standards We as a gathering picked lean and spry strategy for venture the executives. Lithe Software Development procedure is for a task that necessities outrageous spryness in prerequisites. Spry task the board centers around doing the procedure piece-by-piece, as opposed to in one major part like the conventional methodology. Nimble strategy handles venture change and intricacy through correspondence between venture colleagues and end clients. It empowers groups to suitably react to anomaly through short extra work areas, for example, Scrum ‘runs’. These dashes target bringing a well-tried, utilitarian working model. Arranging and changes in configuration happen all through the task dependent on exercises that are found out en route. There’s no disgrace in thinking back to refine the results or highlights of the item at any stage. The work nowadays are increasingly requesting and organizations need to create results of high caliber in a limited ability to focus time. The innovation is moving quickly and the business is globalizing where with the assistance of this innovation it’s simpler for littler and medium size organizations to arrive at the worldwide market. Then again the greater organizations are persistently improving their procedures, items and administrations are probably going to make due in the changing business sector where medium measured and new businesses are blasting at a quick speed. This is the reason the business has begun to enlist an ever increasing number of interdisciplinary groups for the item improvement. An interdisciplinary group comprises of pros of their own fields. A run of the mill interdisciplinary group incorporates experts of innovative work, building, fabricating, advertising, financial matters, expressions, business, and plan. By consolidating people’s qualities in a gathering will increase the value of the item and in the long run to the organization. Use of interdisci Xav-big data plinary groups has quickened the item improvement cycle which will result quick dispatch of the item into the market, brought down the generation costs as those groups will assess every single part of the item before sending it to the assembling stage, it is generally seen that time spend in innovative work stage before sending the item to assembling stage will diminish the expense of the item and stay away from pointless breaks, and even multiplied the evaluated deals. The estimation of interdisciplinary groups is that each part has their very own ability and perspective from their very own field. The assorted variety of the gathering builds access to various sorts of data. A gathering with the individuals all from various foundations can once in a while take care of the issues which will take a long time inside a week or even the issues which feel difficult to split. The gathering individuals likewise gain from one another and might get some significant contacts from different fields. Interestingly, every individual know their job in the gathering as per their own abilities set so they should contribute their greatest exertion. This lets them to concentrate on the parts they’re great at and different individuals will adjust them in the territories where they don’t have the center abilities. This will makes a positive climate and that expands efficiency. A group with various aptitude guarantees that every one of the undertakings of a task are finished. Much after this the interdisciplinary groups must have the ability, information, experience and specialized skill to take care of business. The group needs additionally a brought together objective and a decent pioneer who will lead them to the correct route during the time spent advance Xav-big data ment. Collaboration is troublesome, particularly in a gathering with various aptitudes and ability. The gathering individuals may have contradicting perspectives which can prompt clashes, exercise in futility, and it>
