The Simple Regression Model free essay sample

The simple regression model (SRM) is model for association in the population between an explanatory variable X and response Y. The SRM states that these averages align on a line with intercept ? 0 and slope ? 1:  µy|x = E(Y|X = x) = ? 0 + ? 1x Deviation from the Mean The deviation of observed responses around the conditional means  µy|x are called errors (? ). The error’s equation: ? = y  µy|x Errors can be positive or negative, depending on whether data lie above (positive) or below the conditional means (negative). Because the errors are not observed, the SRM makes three assumptions about them: * Independent. The error for one observation is independent of the error for any other observation. * Equal variance. All errors have the same variance, Var(? ) = 2. * Normal. The errors are normally distributed. If these assumptions hold, then the collection of all possible errors forms a normal population with mean 0 and variance 2, abbreviated ? N (0, 2). Simple Regression Model (SRM) observed values of the response Y are linearly related to values of the explanatory variable X by the equation: y = ? 0 + ? 1x + ? , ? N (0, 2) The observations: 1. re independent of one another, 2. have equal variance 2 around the regression line, and 3. are normally distributed around the regression line. 21. 2 Conditions for the SRM ( Simple Regression Model ) Instead of checking for random residual variation, we have three specific conditions. Checklist for the simple regression model * Is the association between y and x linear? * Have we ruled out obvious lurking variables? Errors appears to be a sample from a normal population. | * Are the errors evidently independent? * Are the variances of the residuals similar? Are the residuals nearly normal? The estimated standard error of b1 substitutes the sample standard deviation of the residuals Se for the standard deviation of the errors , Se (b1) = sen-1 x 1Sx ? Sen x 1Sx The residual standard deviation sits in the numerators of the expression for se (b1). Since the regression line estimates the conditional mean of Y given X, it is the residuals that measure the variation around the mean in regression analysis. The sample size n is again in the dominator. The larger the sample grows, the more information we have and the more precise the estimate of the slope becomes. Confidence Intervals T = b1- ? 1se(b1) If the errors ? is normally distributed or satisfies the CLT condition, then sampling distribution b1 is approximately normal. Since we substitute Se for to calculate the standard error, we use a t-distribution for inference. The 95% confidence interval for the slope ? 1 in the simple regression model is the interval [b1 – t0. 025,n-2 x se(b1), b1 + t0. 025,n-2 x se(b1)] The 95% confidence interval for the intercept ? 0 is [b0 – t0. 025,n-2 x se(b0), b0 + t0. 025,n-2 x se(b0)] Hypothesis Test Equivalent Inferences for the SRM We reject the claim that a parameter in the SRM (? 0 or ? 1) equals zero with 95% confidence (or a 5% chance of a Type I error) if a. Zero lies outside the 95% confidence interval for the parameter; b. The absolute value of the associated t-statistic is larger than t0. 025,n-2 ? 2; or c. The p-value reported with the t-statistic is less than 0. 05. Regression is often used to predict the respons for new, unobserved cases. In this case, the explanatory variables (xnew) is known but the response (ynew) is unknown. To solve this case, the SRM provides a framework that predict ynew and anticipates the accurancy of this prediction. The SRM models implies that ynew is determined by the equation : Ynew = ? 0 + ? 1 xnew + ? new (? new is a random error term that represent the influences of other factors on the new observation). Prediction interval is an interval designed to hold a fraction (usually 95%) of the values of the response for a given value x of the explanatory variable in a regression. The 95% prediction interval for the response ynew in the SRM is the interval [ynew – t0. 025,n-2 se (ynew), ynew – t0. 25+2 se (ynew)] se ynew=se 1+1n+xnew- x2n-1sx2 the standard error of a prediction se (ynew) is tedious to calculate because it adjust for the position of xnew relative to the observed data. The fathers xnew is from x, the longer the prediction interval becomes. Reliability of Prediction Intervals A prediction interval measures the accuracy of predictions of new observations. Provided the SRM (Simple Regression Model) holds, the approximate 95% prediction interval for an observation at x is ynew  ± 2se. Prediction intervals are reliable within the range of observed data, the region in which the approximate interval [y 2se, y + 2se ] holds. Prediction intervals are also sensitive to the assumptions of constant variance and normality. If the variance of the errors around the regression line increases with the size of the prediction, then the prediction intervals will be to narrow for large items. So, before using prediction intervals, verify that residuals of the regression are nearly normal. The method: * Identify x and y * Link b0 and b1 to problem * Describe data. It can be linear, no obvious lurking variable, evidently independent, similar variances, or nearly normal * Check linear condition and lurking variable condition

What Is The Difference Between Ram And The Hard Drive Essay Sample?

What Is The Difference Between Ram And The Hard Drive Essay Sample?What is the difference between ram and the hard drive essay sample? You will see this term being used a lot in your college education. If you are interested in pursuing an MA or PhD degree, you will need to include a great deal of material on paper that has very little on it.Most of us would like to include some of our own work in our own portfolio but the fact is that we really don't have the time to do so. Writing a good paper is not easy. This is why so many students fail to finish an MA or PhD degree.Instead, of teaching you to write an essay about a subject that you know very little about, they may want to help you by giving you a few tips on how to write an essay based on your own experiences. They are going to be using your previous assignments and research as references for you to write your own research. Writing a hard drive essay sample is pretty much exactly the same as writing a ram essay sample. You are s imply going to add a computerized element to your research so that you can show your instructors how to make better use of their instructional time.Many universities, colleges, and universities are now providing their students with a number of resources online that are actually free services. In many cases these resources can be used in conjunction with one another to improve the quality of your instruction.One of the best places to learn how to write an essay based on your own experiences is to use a text generator. You don't even have to be computer literate to use a text generator to turn your research into an effective essay. The primary thing that you have to do is find a way to convert your research into a coherent piece of written content.If you learn how to use a text generator, you will find that it is one of the best resources that you can find for improving your written work. Using a text generator will teach you how to make use of abbreviations and spellings so that you can make your text appear to be formatted more like a person would write it. It will also help you see the best ways to create effective passages and paragraphs that have no background.What is the difference between ram and the hard drive essay sample? It really is not too difficult to find out what is really going on if you spend some time researching the web.

The Changing Face of TV essays

The Changing Face of TV essays African American are living better they were twenty years ago and so our television shows need to reflect that. We now see real people along with the portrayals of African Americans who are lawyers, doctors, and successful entertainers who also, earn major roles where the plots revolve exclusively around them. The quantity of programming devoted to African American culture today, provides us with unlimited choices from which to choose. After careful study, Steinhorn and Diggs-Brown concluded, During the hours when only one show depicts an African American character, we find that the media consistently depicts African Americans as good hard working people in positions of authority. We also see the familiar faces of celebrities selling various products (590-591). While the depiction of African Americans in the media has made great strides in recent years, many of the shows that we know and love today are still infused with negative stereotypes. On the surface, they seem to be sayi ng positive things about African Americans, but underneath they still illustrate the slanted view typical of American TV. When we examine two popular shows, Frasier and Girlfriends we see how the depiction of race has changed and how it has stayed the same, helping prevent an honest depiction of African American culture. We have already established that negative images persist, but they do not represent the African American community as a whole. We now know that class structures within the African American community decide what type of life you will live. Frasier and Girlfriends display different views of African American life and how we communicate. Both shows depict the lives of the upper-middle class, so they are somewhat similar in that respect, but each choose to use different races which is ironic because both are produced by the same person. Change the race of the characters and it c...

Four Ways to Find New Markets

Four Ways to Find New Markets Youve signed up for all possible newsletters that promise to  introduce you to the magazine of your dreams one that pays well,  publishes fast and edits nary a word. Whats more, youve actually  tried all the magazines touted Or perhaps youve exhausted your permissible quota of stories that can  be submitted to these dream magazines. (Two in a year. Yeah, right.  What are you supposed to do for the remaining ten months?) Or perhaps youve sold first rights and would now like to sell  reprints to other magazines to make a quick, painless buck. Whatever the reason, you need more wonderful magazines to submit  stories to. Only, where do you find them? With more than 5,500 markets in my personal database, Ive become  something of an expert in sniffing out potential venues for  publication. Want to know my secret? Actually there are four: 1. Peek into your own backyard. Has your work been published online? Web magazines often have a  section that hyperlinks to other similar e-zines. It goes 2. Take a helping hand from your competitors. Diligently read the

PRE-LAUNCH DECISIONS WHICH INFLUENCE INNOVATION SUCCESS Essay

PRE-LAUNCH DECISIONS WHICH INFLUENCE INNOVATION SUCCESS - Essay Example The actors of the manufacturing world adapt to the innovation for increasing the availability of the complementary products. This in turn enhances the value of the innovation. The subsequent adopters reinforce this process for the promoting the double loop cycle (Frattini, 81-120). Using this system and allowing the early adopters and the network development personnel enhances the value of the innovation for the user. This further promotes long term strategic partnership between the members of the adoption network. This process also shares the risk and supports the systemic innovation. Different innovation products like the Palm Pilot, Apple and Nintendo have used this technique for reducing this risk associated with the innovation. In some of the cases such companies have also refused to share any sort of partnerships with the competitors and yet share the innovation. This leads to a commercial relationship and leads to potential profits realized by the organization. Adapting to thi s practice the companies commercializes their innovation which leads to the subsequent future benefits. Due to the increasing high tech innovations the target market comprises of the people who resist change. This leads to uncertainty when evaluating the opportunity. The willingness of the early adopters to buy the products is not backed by the critical members which are part of the adoption network. This represents signals to the later adopters and hence reduces resistance and uncertainty. Hence this shows the role of early adopters and network developments in the market acceptance process of innovation. Question # 2: Compare and contrast the critical factors that impact successful and unsuccessful innovations; pay particular attention to timing and positioning. The critical factors which impact on the successful and unsuccessful innovations are timing, targeting and positioning, inter-firm relationships, product, distribution, advertising and promotion and pricing. Comparing the p rocess signifies the success and failures of the process. For the inter-firm relationship it is signified that support is required from the critical administrators of the process. This ultimately leads to enhancing the value of the innovation. Increasing the availability of the complementary products will enhance the potential adoption for choosing the purchase of the innovation. Different strategic policies are initiated for initiating a long term partnership. The contributing role of the adoption networks also refers to content based innovations and promotes use of creative software’s for application development (Frattini, 81-120). Timing is considered as one of the most critical factors. The timing with which the innovations are formed is important for determining the degree of support which is ensured to the innovation. The analysis shows that often the firms act to postpone the establishment of strategic alliances. Once the innovation has been launched in the markets the n the critical players engaged with the product take the measures for promoting it. Timing is also critical because in certain situations the product fails to generate the sales in a particular segment. Example of such a situation is that Sony refused to partner with electronic outlets. Similarly the targeting and positioning of the innovations also plays a vital role. A firm easily succeeds in orchestrating the support from the adoption network players. The firms appropriately select the target market and they position the product accordingly for attracting the right set of customers. in some cases the response from the

Visit a museum or gallery exhibition or attend a theater, dance, or Essay

Visit a museum or gallery exhibition or attend a theater, dance, or musical performance - Essay Example There was something about the fact that they were elevated above my typical line of vision. Craning my neck, I enjoyed the slow natural rotation of each of the mobiles. Some of the shapes conveyed a sense of whimsy while others had a more threatening feel. After many minutes, I was ready to move on, until I notice how the light played on each of the mobiles and the resulting shadows that were cast upon the walls of the circular room. The shadows created by the lighting installation gave an entirely different dimension to the mobile installation. As the mobiles rotates freely, the shadows cast upon the walls displayed a motion that seemed to be more active than the perceived motion of the mobile. The slightest rotation of the mobile would send a shadow racing across the wall. In addition to this, the shadows were constantly transforming in shape and sharpness. Due to the play of the lighting and the three dimensional construction of the mobiles, some shadows were crisp edged and dark while others, cast from the same mobile resembled amorphous grey smudges. The constant interplay of shadows of different value created movement and action that belied the slowly rotating mobiles mounted above my head. The second exhibition I attended was the Matisse Cutouts in the next room. For the last fifteen years of his life, Matisse rediscovered his passion and creativity by constructing colorful paper cutouts and displaying them on the walls of his studio. Matisse has suffered several personal setbacks that had left him physically and mentally exhausted. He no longer felt inspired to create as a result. While resting, he began to work with the idea of cutting into color to create paper shapes that melded the ideas of painting, drawing and sculpture. The resulting work is interesting to behold, not just because the shapes are beautiful, but also because the scale of the paper cutouts is massive. The most interesting of the

Volcanic Activity at Yellowstone :: essays research papers

Yellowstone is a national park covering 3,468 square miles in Wyoming, Idaho, and Montana and it is elevated 8,000 feet from the ground on a plateau. But is there still present volcanic hazard in Yellowstone? The park is covered with over 10,000 geysers, hot springs, mud pots, and travertine terraces, perhaps caused by a ?hot spot? that it overlies. A violent history suggests equally as devastating future volcanic activity, underground forces are causing the landscape to change and geysers to become more active. The real question is, if a super volcanic explosion took place, would human life exist as we know it ever again? The history of volcanic activity at Yellowstone starts with its first eruption at Huckleberry Ridge 2.1 million years ago, the leftovers reached as far as Iowa and central Texas. Then 800,000 years later, another eruption took place in Mesa Falls creating Henry Fork Caldera near Park, Montana. The last eruption took place 630,000 years ago, called the Lava Creek eruption, spewing 240 cubic miles of debris, and spreading as far as Louisiana and California. Hidden underneath the park, powerful volcanic, magnetic, and hydrothermal forces are reforming the land. Several earthquakes, uplifting, and subsidence of the landscape proves that these powers exist. Recent studies have caused scientists to think that Yellowstone could be growing larger as flowing molten rock builds up below the ground. In a period of 10 years, the volcano has risen 5 inches, not a significantly detectable difference, but it may have split the ground in the Norris Geyser Bassin that could reawaken some of the geysers, like the Steamboat. In spite of this newly found information, scientists do not speculate the volcano erupting any time soon, but with time, it will end with a super natural disaster, destroying everything in its path When Yellowstone does erupt, the United states could be covered in 3 feet of ash from the eruption. First, the pyroclastic flow would swallow most of Wyoming, Idaho, and Montana. Then, like Yellowstone eruptions have done before, the world would fall into a freezing, winter lasting around 10 years. Mass famine would take place all around the world as the eruption would have devastated the agriculture, effecting the food.