Spss Regression

Simple Linear Regression in SPSS 1. STAT 314 Ten Corvettes between 1 and 6 years old were randomly selected from last year’s sales records in Virginia Beach, Virginia. The following data were obtained, where x denotes age, in years, and y denotes sales price, in hundreds of dollars. x y a. b. c. d. e. f. g. h. i. j. k. l. m. 6 125 6 115 6 130 4 160 2 219 5 150 4 190 5 163 1 260 2 260 Graph the data in a scatterplot to determine if there is a possible linear relationship. Compute and interpret the linear correlation coefficient, r. Determine the regression equation for the data.Graph the regression equation and the data points. Identify outliers and potential influential observations. Compute and interpret the coefficient of determination, r2. Obtain the residuals and create a residual plot. Decide whether it is reasonable to consider that the assumptions for regression analysis are met by the variables in questions. At the 5% significance level, do the data provide sufficient evidence to conclude that the slope of the population regression line is not 0 and, hence, that age is useful as a predictor of sales price for Corvettes? Obtain and interpret a 95% confidence interval for the slope, ? of the population regression line that relates age to sales price for Corvettes. Obtain a point estimate for the mean sales price of all 4-year-old Corvettes. Determine a 95% confidence interval for the mean sales price of all 4-year-old Corvettes. Find the predicted sales price of Jack Smith’s 4-year-old Corvette. Determine a 95% prediction interval for the sales price of Jack Smith’s 4-year-old Corvette. Note that the following steps are not required for all analyses†¦only perform the necessary steps to complete your problem. Use the above steps as a guide to the correct SPSS steps. 1.Enter the age values into one variable and the corresponding sales price values into another variable (see figure, below). 2. Select Graphs ? Legacy Dialogs ? Scatte r/Dot†¦ (select Simple then click the Define button) with the Y Axis variable (Price) and the X Axis variable (Age) entered (see figures, below). Click â€Å"Titles†¦Ã¢â‚¬  to enter a descriptive title for your graph, and click â€Å"Continue†. Click â€Å"OK†. Your output should look similar to the figure below. a. Graph the data in a scatterplot to determine if there is a possible linear relationship. The points seem to follow a somewhat linear pattern with a negative slope. . Select Analyze ? Correlate ? Bivariate†¦ (see figure, below). 4. Select â€Å"Age† and â€Å"Price† as the variables, select â€Å"Pearson† as the correlation coefficient, and click â€Å" â€Å"OK† (see the left figure, below). b. Compute and interpret the linear correlation coefficient, r. The correlation coefficient is –0. 9679 (see the right figure, above). This value of r suggests a strong negative linear correlation since the value is n egative and close to –1. Since the above value of r suggests a strong negative linear correlation, the data points should be clustered closely about a negatively sloping regression line.This is consistent with the graph obtained above. Therefore, since we see a strong negative linear relationship between Age and Price, linear regression analysis can continue. 5. Since we eventually want to predict the price of 4-year-old Corvettes (parts j–m), enter the number â€Å"4† in the â€Å"Age† variable column of the data window after the last row. Enter a â€Å". † for the corresponding â€Å"Price† variable value (this lets SPSS know that we want a prediction for this value and not to include the value in any other computations) (see left figure, below). . Select Analyze ? Regression ? Linear†¦ (see right figure, above). 7. Select â€Å"Price† as the dependent variable and â€Å"Age† as the independent variable (see upperleft fi gure, below). Click â€Å"Statistics†, select â€Å"Estimates† and â€Å"Confidence Intervals† for the regression coefficients, select â€Å"Model fit† to obtain r2, and click â€Å"Continue† (see upper-right figure, below). Click â€Å"Plots†¦Ã¢â‚¬ , select â€Å"Normal Probability Plot† of the residuals, and click â€Å"Continue† (see lower-left figure, below).Click â€Å"Save†¦Ã¢â‚¬ , select â€Å"Unstandardized† predicted values, select â€Å"Unstandardized† and â€Å"Studentized† residuals, select â€Å"Mean† (to obtain a confidence interval†¦output in the Data Window) and â€Å"Individual† (to obtain a prediction interval†¦output in the Data Window) at the 95% level (or whatever level the problem requires), and click â€Å"Continue† (see lower-right figure, below). Click â€Å"OK†. The output from this procedure is extensive and will be shown in parts in th e following answers. c. Determine the regression equation for the data. From above, the regression equation is: Price = 29160. 1942 – (2790. 2913)(Age). 8.From within the output window, double-click on the scatterplot to enter Chart Editor mode. From the â€Å"Elements† menu, select â€Å"Fit Line at Total†. Click the close box. Now your scatterplot displays the linear regression line computed above. Graph the regression equation and the data points. d. e. Identify outliers and potential influential observations. There do not appear to be any points that lie far from the cluster of data points or far from the regression line; thus there are no possible outliers or influential observations. f. Compute and interpret the coefficient of determination, r2. The coefficient of determination is 0. 368; therefore, about 93. 68% of the variation in the price data is explained by age. The regression equation appears to be very useful for making predictions since the value of r 2 is close to 1. 9. The residuals and standardized values (as well as the predicted values, the confidence interval endpoints, and the prediction interval endpoints) can be found in the data window. 10. To create a residual plot, select Graphs ? Legacy Dialogs ? Scatter/Dot†¦ (Simple) with the residuals (RES_1) as the Y Axis variable and Age as the X Axis variable. Click â€Å"Titles†¦Ã¢â‚¬  to enter â€Å"Residual Plot† as the title for your graph, and click â€Å"Continue†.Click â€Å"OK†. Double-click the resulting graph in the output window, select â€Å"Options† ? â€Å"Y Axis Reference Line†, select the â€Å"Reference Line† tab in the properties window, add position of line â€Å"0†, and click â€Å"Apply†. Click the close box to exit the chart editor (see left plot, below). 11. To create a studentized residual plot (what the textbook calls a standardized residual plot), select Graphs ? Legacy Dialogs ? Scatter/Dot†¦ (Simple) with the studentized residuals (SRES_1) as the Y Axis variable and Age as the X Axis variable. Click â€Å"Titles†¦Ã¢â‚¬  to enter â€Å"Studentized Residual Plot† as the title for your graph, and click â€Å"Continue†.Click â€Å"OK†. Double-click the resulting graph in the output window, select â€Å"Options† ? â€Å"Y Axis Reference Line†, select the â€Å"Reference Line† tab in the properties window, add position of line â€Å"0†, and click â€Å"Apply†. If 2 and/or -2 are in the range covered by the y-axis, repeat the last steps to add a reference line at â€Å"2† and â€Å"-2† (see right plot, above); any points that are not between these lines are considered potential outliers. If 3 and/or -3 are in the range covered by the y-axis, repeat the last steps to add a reference line at â€Å"3† and â€Å"-3†; any points that are beyond these lines are considered ou tliers. 2. To assess the normality of the residuals, consult the P-P Plot from the regression output. g. Obtain the residuals and create a residual plot. Decide whether it is reasonable to consider that the assumptions for regression analysis are met by the variables in questions. The residual plot shows a random scatter of the points (independence) with a constant spread (constant variance). The studentized residual plot shows a random scatter of the points (independence) with a constant spread (constant variance) with no values beyond the  ±2 standard deviation reference lines (no outliers).The normal probability plot of the residuals shows the points close to a diagonal line; therefore, the residuals appear to be approximately normally distributed. Thus, the assumptions for regression analysis appear to be met. h. At the 10% significance level, do the data provide sufficient evidence to conclude that the slope of the population regression line is not 0 and, hence, that age is u seful as a predictor of sales price for Corvettes? Step 1: Hypotheses H 0 : ! = 0 (Age is not a useful predictor of price. ) H a : ! † 0 (Age is a useful predictor of price. ) Step 2: Step 3: Step 4: Significance Level ! 0. 05 Critical Value(s) and Rejection Region(s) Reject the null hypothesis if p-value ? 0. 05. Test Statistic (choose either the T-test method or the F-test method†¦not both) T = –10. 8873, and p-value = 0. 00000448 Step 5: Step 6: F = 118. 5330, and p-value = 0. 00000448 Conclusion Since p-value = 0. 00000448 ? 0. 05, we shall reject the null hypothesis. State conclusion in words At the ! = 0. 05 level of significance, there exists enough evidence to conclude that the slope of the population regression line is not zero and, hence, that age is useful as a predictor of price for Corvettes. . Obtain and interpret a 95% confidence interval for the slope, ? , of the population regression line that relates age to sales price for Corvettes. We are 95% co nfident that the slope of the true regression line is somewhere between –3381. 2946 and –2199. 2880. In other words, we are 95% confident that for every year older Corvettes get, their average price decreases somewhere between $3,381. 2946 and $2,199. 2880. j. Obtain a point estimate for the mean sales price of all 4-year-old Corvettes. The point estimate (PRE_1) is 17999. 0291 dollars ($17,999. 0291). k.Determine a 95% confidence interval for the mean sales price of all 4-year-old Corvettes. We are 95% confident that the mean sales price of all four-year-old Corvettes is somewhere between $16,958. 4604 (LMCI_1) and $19,039. 5978 (UMCI_1). l. Find the predicted sales price of Jack Smith’s selected 4-year-old Corvette. The predicted sales price is 17999. 0291 dollars ($17,999. 0291). m. Determine a 95% prediction interval for the sales price of Jack Smith’s 4-year-old Corvette. We are 95% certain that the individual sales price of Jack Smith? s Corvette wi ll be somewhere between $14,552. 9173 (LICI_1) and $21,445. 1410 (UICI_1).

Frankenstein, Blade Runner and the Natural World

Continually throughout history humanity’s connection to the natural world has been probed, celebrated, mocked and forgotten in a haphazard cycle that has been classified as human nature. Through a comparison of Mary Shelley’s 19th Century didactic novel, ‘Frankenstein’ (the Modern Prometheus) and the director’s cut of Ridley Scott’s ‘Blade Runner’, a common conception of man’s place amongst nature is posed as being submissive to her dominance.Though each text shares the same values each represents its core concepts in a manner inimitable to its context, ultimately critiquing the respective society’s, bringing to light the fears that the majority of society refused to acknowledge at the time. These fears centre mainly around three broad concepts; scientific discovery, industrial development and religion, which collectively invite consideration of humanity’s unabridged connection with the natural world and how i t has been altered over time.In the spirit of Enlightenment, a large cultural movement in the pre-19th century world, Shelley conceived Frankenstein and, in effect, his creation. The Enlightenment movement encouraged people to turn away from faith and to start relying more on reason and the answers developments in science were beginning to supply. â€Å"A mummy again endued with animation could not be so hideous as that wretch. † The juxtaposition of the Creatures unnatural image with the romantic values of the sublime and creative genius characterises the monumental shift away from the natural.The death of her protagonist, Victor Frankenstein, represents the expectations the romantic writer has for the enlightenment movement, alluding to the inevitable doom it will bring upon humanity. By creating a juxtaposed image between Frankenstein, who is repeatedly surrounded by pejorative terms such as ‘suffer’, ‘malice’ and ‘bitter’, and his br other Ernest, characterising the latter as ‘full of activity and spirit’, Shelley places Ernest in the role of Romanticism whilst Frankenstein personifies the Enlightenment movement.Their contrasting connections to the natural world and their subsequent lives, permits Shelley to critique her own context and the ideals within it. Her views on Romanticism and Enlightenment are similar to that of Rousseau, a known philosopher who suggested that ‘†¦nothing is so gentle as man in his primitive state, when placed by nature at an equal distance from the stupidity of brutes and the fatal enlightenment of civil man. ’ This suggests that humanity’s connection with nature is essential to ensure harmony within ociety and in effect it’s survival in the world. Reinforcing this theory, Blade Runner, presents an image of this corrupted harmony and its effects on humanity. Ridley Scott’s text reveals that within his time, 178 years after ‘Fra nkenstein’, scientific development still held the same destructive concerns. However, by the use of film rather than text, Scott represents the fears of his society in a much more vivid approach, preventing them from being so easily disregarded.Current technology now allowed scientists to experiment in the world of robotics and areas such as IVF, leading many to question how this would affect humanity’s natural roles within society. This is demonstrated as Scott blurs the lines between what makes a human truly human. He does this by giving the replicants human emotions and unique identities. Pris’ words ‘I think Sebastian, therefore I am’ reinforce this idea while also alluding to the evolving knowledge and skills of the artificial beings, their natural abilities to adapt and progress.These developments in science within the film have dismal consequences, ones which Scott fears for his own world, and the continuous downfall of rain is just one prese ntation of this, symbolic of mother nature grieving over her destruction. As times were changing in both contexts and new sciences were explored people repeatedly questioned their faith, causing many religious debates and conflicts. ‘Frankenstein’ represents common battles of moral and God, going so far as to be known as the Modern Prometheus.The reference to the Promethean myth foreshadows the consequences Frankenstein will undoubtedly have to face. Blinded by his own ambition and dreams of glory and fame he endeavours to take on the role of God by creating life and disrupting natural order. In creating his monster Frankenstein also usurps the natural role of women as child bearers, questioning their place and use within humanity. â€Å"A new species would bless me as its creator and source; many happy and excellent natures would owe their being to me. The juxtaposition of the phrase ‘excellent natures’ with the clearly unnatural give insight into the one -tracked desires of Frankenstein, not pausing to consider the moral issues surrounding his experiments. However, he ironically seems to blame God and fate for the destructive course of his life, telling Walton ‘destiny was too potent, and her immutable laws had decreed my utter and terrible destruction. ’ Faith subsequently had a ambiguous impact on humanity’s connection to nature, representing the ideals of natural order and the consequences of destroying it’s structure.Similarly, the role of God is also obscured in the dark scenes of Blade Runner, stemming from the lack of nature. Religious allusions are rich throughout the text, beginning within the first sequence when syncopated bursts of flames create an image resembling Dante’s hell, suggesting hell on earth. â€Å"A new life awaits you, the chance to begin again in the New World. † After destroying their own world the Tyrell corporations promises of bigger, better things are seen as a missionary act, the answer to humanity’s problems. This earns Tyrell levels of power unequitable on Earth and lead him to believe himself to be a God.The sharp cut lines and magnitude of the Tyrell building reinforces these implications as it looms over the city, placing him above the rest of humanity. However, the triumphant forces of nature come through in the final scenes as Tyrell meets his end, and natural order begins to be rectified with the death of Pris and Batty. The white light illuminating Batty’s form as his body shuts down gives him a godly image, supported by the nail protruding through his hand and the white dove that flies away, a symbol of peace and hope for restoration.This scene reinforces natures purity and the extent of its healing powers in contrast with humanity’s destructive impact on its elements. Mary Shelley and Ridley each created monumental texts with the common concepts of scientific development, industrialisation and religion. Bot h explore how humanity’s connection with the natural world is distorted and overshadowed by the influences of modern advances and opportunities, leading to its exploitation and neglect.

Area and Volume

Previous exam questions on area between functions and volumes of solids. 1. Let f(x) = cos(x2) and g(x) = ex, for –1. 5 ? x ? 0. 5. Find the area of the region enclosed by the graphs of f and g. (Total 6 marks) 2. Let f(x) = Aekx + 3. Part of the graph of f is shown below. The y-intercept is at (0, 13). (a)Show that A =10. (2) (b)Given that f(15) = 3. 49 (correct to 3 significant figures), find the value of k. (3) (c)(i)Using your value of k, find f? (x). (ii)Hence, explain why f is a decreasing function. iii)Write down the equation of the horizontal asymptote of the graph f. (5) Let g(x) = –x2 + 12x – 24. (d)Find the area enclosed by the graphs of f and g. (6) (Total 16 marks) 3. The following diagram shows the graphs of f (x) = ln (3x – 2) + 1 and g (x) = – 4 cos (0. 5x) + 2, for 1 ? x ? 10. (a)Let A be the area of the region enclosed by the curves of f and g. (i)Find an expression for A. (ii)Calculate the value of A. (6) (b)(i)Find f ? (x). (ii)F ind g? (x). (4) c)There are two values of x for which the gradient of f is equal to the gradient of g. Find both these values of x. (4) (Total 14 marks) 4. The graph of f(x) = , for –2 ? x ? 2, is shown below. The region enclosed by the curve of f and the x-axis is rotated 360Â ° about the x-axis. Find the volume of the solid formed. (Total 6 marks) 5. The graph of y = between x = 0 and x = a is rotated 360Â ° about the x-axis. The volume of the solid formed is 32?. Find the value of a. (Total 7 marks)

Marketing is The management process of anticipating, identifying and Essay - 1

Marketing is The management process of anticipating, identifying and satisfying customer requirements profitably (CIM, 2001) - Essay Example It involves formulation and communication of information that can generate utility to different stakeholders to a subject entity and such stakeholders may be customers, business associates, the community, and contractual parties to an institution’s activities. In addition, the scope of the definition of marketing identifies a dual approach to information transfer between an entity and its stakeholders (Taylor 2010, p. 152). This definition is valid because it identifies with the American Marketing Association’s (AMA’s) definition. The CIM’s definition of marketing focuses on customers’ utility and organizations’ profitability. Even though the AMA’s definition does not focus on profit motive for organization’s engagement in marketing, this is trivial from the scope of corporate ventures that profit motive drives. Such a scope validates CIM’s definition of marketing as a strategy to profit optimization by business organization and is consistent with organizations’ initiatives for efficiencies and effectiveness that can results to low production costs for higher profit margins and economies of scale advantage. CIM also identifies customer utility as a driver to marketing initiative and this is reflexive of the definition of marketing according to AMA. According to AMA, the focus of marketing is to meet customers’ needs, at individual an d societal levels. The CIM’s definition of marketing also identifies, though not directly, associated activities with marketing that AMA outlines. Anticipating and identifying customers’ needs, for example, involves exploration of background information into customers’ needs for creation of information or commodities while satisfying such needs relates to communication and transfer of utilities for customers’ satisfaction. CIM’s definition is further consistent with AMA’s previous definitions of marketing that that identified focus on business undertakings and development of values for

Question 10 Essay Example | Topics and Well Written Essays - 250 words

Question 10 - Essay Example It offers services and products not only to U.S Government, but to the Intelligence Community, Industry Partners, the Defense Department, Coalition allies and Selected Partners. Furthermore, it also gives strategic, tactical, critical, and valuable information to war fighters and war planners in United States Government. (NSA/CSS| 2011) A high quantity of discretion and privacy is the primary aspect of National Security Agency/Central Security Service as a chief member of Community of Intelligence. The mission of National Security Agency/Central Security Service is Assurance of Information and sees this Assurance as an alarming challenge to protect the information from foreign enemies from getting entrance to classified or sensitive information about national security. It also has a mission of Signals Intelligence which gathers, processes, and distributes information related to information from foreign pressures for both intelligence and counterintelligence reasons and also to carry out operations of the United States military. This Agency also allows the Network Warfare to assist encounter the terrorist organizations both in the home country as well as abroad. (NSA/CSS| 2011) It works in collaboration with the laws of United States and also guards the confidentiality and national autonomy. It exists to safeguard the nation whenever it needs it. (Centre for Strategic and International