The Challenges of Raising Tobacco and Alcohol Taxes

Will raising tobacco and alcohol taxes decrease consumers and benefit to fund states and people for the rising medical costs? It has been said a lot about the dangers of smoking and drinking. We hear about it everyday in the mass media and from health professionals. It is hard to see people losing their voice, being unable to work and in the end dying because of cancer. It is also painful to watch the whole family from a household dying as a result of their car being hit by drunk driver. There are lots of children, adults and hardworking people who died as a result of drinking and driving. McLLelan Deborah , on Washington News Letter Section states about tobacco and alcohol: Cigarettes kill close to 435,000 Americans and cost society tens of billions of dollars annually. Alcohol use causes more than 100,000 deaths each year in the U.S. and is related to a number of health and Social problems. Econometric studies estimate that a $2 per cigarette pack increase would prevent roughly 2 million premature deaths over time by deterring youths from starting to smoke and encouraging smokers to quit. Increases in alcohol prices have also been shown to keep youths from drinking. (Nations Health Mar93, Vol. 23 Issue 3, p4) The fight against this problem has to be an ongoing process. It is a major issue that involves lives. Increasing taxes on tobacco and alcohol improves the health of people and can benefit the government and people to finance the rising medical cost. AlthoughShow MoreRelatedRaising Taxes on Tobacco and Alcohol1637 Words   |  6 PagesRaising taxes on tobacco and alcohol The harmful effect of tobacco and alcohol are well profound and experienced in the daily lives of people across the world. It has been mentioned and medically proven that some of the deadliest conditions like liver cirrhosis and cancers are associated with the consumption of these two substances. The rate of the abuse apparently is increasing with the heightened networking of the globe and the use of these two substances has fast moved to the abuse levelsRead MoreEconomy: Taxes are Good Especially at the Macroeconomic Level684 Words   |  3 PagesTaxes– the word which sent ripple effects once the mind interpreted the word. A surcharge, something paid above and beyond the good you’re paying for. At times one might burst boughs of anger in coloured word as your initial calculations on what you were going to pay are wrong. Wait a minute, those taxes are working for us– or are they? If you look at the economy at a macro level, it doesn’t take a genius to see that taxes are generally good. When looking at the expenditure approach GDP=C+I+G+NxRead MoreIncrease Taxation Of Tobacco Products On South Korea And Reduce The Levels Of Noncommunicable Diseases1733 Words   |  7 PagesAmy Tseng G H 511: Problems in Global Health Critical Analysis Paper December 2, 2014 Word Count: 1,536 Increase taxation of tobacco products in South Korea to reduce the levels of noncommunicable diseases Introduction and Background One of the major global public health challenges of the 21st century is noncommunicable diseases (NCDs). Current global mortality from NCDs remains exceedingly high and continues to increase. According to World Health Organization (WHO) 2014 estimates, 38 millionRead MoreThe $ 6.7 Million Budget Gap For The Next Fiscal Year830 Words   |  4 Pagessuggestion of what you, our Mayor, can do to meet the next fiscal year budget. Piggybacking a considerable sales tax of  ¾ cent onto the state’s current rate of 8% is a good idea. Piggybacking is the best option I would recommend to you as a method of raising the revenue. The attachment of the tax would make the people pay more than they do while making sales. The idea can raise revenue that can be helpful to meet the budget. Te people will have to pay as every day people make sales and therefore cannotRead MoreThe Effects of Lowering the Drinking Age to 181126 Words   |  5 PagesRhetoric and Composition 15 December 2012 Lowering The Drinking Age Alcohol is considered to be a large problem in society today. Especially with young adults between the ages of eighteen and twenty-one. Which presents the question of whether or not the drinking age should be lowered. Lowering the legal drinking age to eighteen would have positive and negative influences on society. Positive through raising more government taxes and keep high school age and young college students out of troubleRead MoreEssay on Higher Education and Financial Aid from the Government1667 Words   |  7 Pagesvery significant changes have been made by our government offering improved financial aid to current and future students, more can still be done. Our politicians could increase the Pell Grant maximum to coincide with rising tuition costs, increase taxes on irrelevant goods and services to provide students with more direct funding, set up a â€Å"reward system† that would place more responsibility on the students (rather than themselves), and most impo rtantly, our two main parties in office need to agreeRead MoreEffect of Cigarette Smoking Essay2834 Words   |  12 Pagespresented with few grammatical and spelling errors, correctly referenced with Harvard reference style | | | | | | | General Comments 1st Marker Deborah Richardson 2nd Marker Introduction This presentation evaluates the impact of tobacco smoking in Nigeria with a proposed structured strategy based on theoretical approaches and public Health models to tackle this complex Health problem in a bid to improve and protect Health. Until recently, non communicable diseases stillRead More Globalization Has A Negative Impact on Global Health1799 Words   |  8 Pageswill examine how globalisation has helped alcohol and tobacco trade around the world and in doing so affected health, how globalization has enabled the global community to combat these issues and an estimation of alcohol and tobacco consumption in different countries. This essay will also contain statistics from the World Health Organization based on alcohol and tobacco to illustrate the impact of globalisation. Alcohol: The question as to when alcohol was invented is still unknown, but the discoveryRead MoreAnti Smoking Programs For Smoking1589 Words   |  7 Pagesother campaigns have taken on the challenge of combatting anti-smoking with the tobacco industry’s promotion. The â€Å"truth† campaign, specifically, imposed an early and effective model for anti-smoking programs to follow, therefore making it highly successful. The â€Å"truth† campaign is one of the most recent large-scale national anti-smoking programs used to change attitudes and beliefs towards smoking. In 1998, the Florida Department of Health launched this tobacco prevention program that featured aRead MoreAmerica s Fiscal 2017 Budget1719 Words   |  7 Pagesas Louisiana was awash in one-time revenue, including federal funding to the state to aid recovery from disasters such as hurricanes Katrina and Gustav. Critics of the state s use of one-time revenue said it shielded the effects of lowering income taxes that caused a long-term structural deficit. Now, the rains in Louisiana have added to its revenue misery and exacerbated the vulnerability to revenue weakness in the natural resources sector, or, as Marcia Howard wrote: Clearly, there are states

Taking a Look at Anorexia Nervosa - 1158 Words

Anorexia Sickness can quickly become a disease. An eating disorder called anorexia nervosa begins as a type of diet but turns into a disease that can severely affect many aspects of your life. This occurs when people reach the point of starvation because they are overly conscious of their weight, even though they may be dangerously underweight. When someone becomes obsessed with their self-image, action must be taken to provide the best treatment for them. Anorexia can become a serious problem that will change the way you think, act and feel. Because of various factors, individuals are devastated emotionally mentally by anorexia. One factor that triggers anorexia begins at an early age. Particular childhood events can lead to eating†¦show more content†¦In other cultures, eating disorders are just as ubiquitous. A study was done by Osvold Sodowsky, and it proved that Black and Native American women who were more accommodating with the American culture showed more symptoms o f anorexia than those who were less accepting of the white American way of living (Northwestern University). This proves that the impact from the media, especially in America, provides a hope for something that isn’t reachable. In past years, it was said that anorexia was most commonly found in upper-middle class White women, but over time, women of different ethnicities are also commonly confronted with anorexia. (Duckworth, Freedman). It is possible to lose enough weight to fit the standard that is set, but can hurt your life in so many different ways. Eating disorders are not just about food and weight; they affect someone both psychologically and emotionally. â€Å"Anorexics punish themselves for their perceived failures and self-hatred by restricting their food intake.† (Engel). Although this may be the case, people with anorexia don’t just take food from their lives, the fact that they have self-hatred to trigger it causes many more complications and long-term effects. Clearly, anorexia is not just a weight issue. Individuals mainly use food to control how they are feeling if they are placed in a conflict or feel insecure.Show MoreRelatedTaking a Look at Anorexia Nervosa1613 Words   |  7 Pagesthat I have learnt a lot about eating disorders and anorexia nervosa in particular. I researched the DSM V diagnostic criteria for anorexia nervosa. The criteria that must be met include an intense fear of gaining weight (even if the patient is severely underweight), restriction of calorie intake relative to requirements leading to a significantly low weight and an altered perception of one’s own body weight/shape. Sufferers of anorexia nervosa can be subdivided into two types: restricting (who cutRead MoreAnorexia Nervosa, Bulimia, And Binge Eating1694 Words   |  7 Pagesactivities, eating disorders are becoming more and more common. There are three main types: anorexia nervosa, bulimia, and binge eating. Binge eating is when you consume large amounts of food at one time, following the intake with no attempt to prevent weight gain. Bulimia is when you consume large amounts of food at one time, followed by an attempt to prevent weight gain, such as self-induced vomiting. Anorexia Nervosa is when you limit your food intake to little-to-none with the outcome of weight thatRead MoreThe Dangerous Effects of Eating Disorders1100 Words   |  5 Pagesthat you eat and how much you weigh, you often focus on little else (http://www.mayoclinic.org/diseases-conditions/eating-disorders/basics/def inition/con-20033575 ). There are three main types of eating disorders. Anorexia nervosa is the fear of gaining weight. If you have bulimia nervosa, you eat large amounts very quickly, and then you purge. Lastly, binge eating is where you feel out of control and you eat, and eat, and eat, and you cannot stop. Eating disorders can cause serious physical problemsRead MoreAnorexia Nervos Eating Disorders Association1013 Words   |  5 PagesIntroduction Anorexia nervosa is an eating disorder that affects about 0.5 to 1 percent of women in the United States today. (Anorexia Nervosa | National Eating Disorders Association) While, that may not seem like a lot of people are suffering from Anorexia nervosa it has received a significant amount of attention due to the consequences of developing this disorder. For example, it is reported that five to twenty percent of people who have Anorexia Nervosa will eventually succumb to theirRead MoreEating Disorders And Eating Disorder1410 Words   |  6 Pages as defined by our text book for class, is psychological disturbances that lead to certain physiological changes and serious health complications. The three most common and most easily identifiable forms of eating disorders include anorexia nervosa, bulimia nervosa, and binge eating disorder. While most people who have eating disorders tend to be women from white middle-class upper-class families, eating disorders span social class, ge nder, race, and ethnic backgrounds (Floyd, Mimms, YeldingRead MoreEating Disorders Among Young Adults1015 Words   |  5 Pagessociety seeing famous people look like that it makes people take drastic measures to become skinny like them. Some people just don’t eat, others eat too much and then they make themselves throw up, and others don’t eat and then go exercise too much. Also we live in a society that is surrounded by food. In the United States there is a fast food restaurant on almost every corner and yet there is still an issue with eating disorders such as anorexia nervosa, bulimia nervosa, and binge eating. When itRead MoreEating Disorders : Anorexia Nervosa998 Words   |  4 Pageseven social factors. Their main concern tends to focus on the amount of weight but yet gorge on varieties of unhealthy high calorie products (silverthorne1). In consequence females start to have Anorexia Nervosa or even Bulimia Nervosa. Even though both disorders are dangerous similarity Anorexia Nervosa and Bulimia have common symptoms on an individual’s health and can even lead to termination of their life. Initially both disorders can be caused by becoming obsessed with unhealthy foods such asRead MoreEating Disorders : Anorexia Nervosa1443 Words   |  6 Pageseating disorders can be characterized in three ways which include anorexia nervosa, bulimia nervosa, and binge-eating disorder. Anorexia nervosa can be further broken down into two types which are anorexia nervosa restricting type, and anorexia nervosa binge/purge type. Eating disorders if approached early enough can be reversed with no damage or very minimal damage to the person. One characteristic of an eating disorder is anorexia nervosa. This characteristic as described by Hoeksema (2014) is seenRead MoreThe Risks And The Management Of Adolescents With Eating Disorders1218 Words   |  5 Pageswas supplied by the University of North Carolina at Chapel Hill School of Dentistry. The ultimate goal of this research was to educate dental professionals on anorexia nervosa and bulimia nervosa and how to identify the predisposing factors. To begin, Hicks and Roberts start off by start off by telling us that statistically speaking anorexia and bulimia are serious medical conditions that most commonly effect adolescents and young adults. In 2014, 70 million people worldwide showed clinical signsRead MoreEating Disorders and the Media941 Words   |  4 PagesAccording to the National Association of Anorexia Nervosa and Associated Disorders, â€Å"the body type portrayed in advertising as the ideals is possessed naturally by only 5% of American females.† (â€Å"ANAD†) Body image has been a controversial theme because of the influence of the media. It is a widely known fact that eating disorder cases are on the rise. The concept of body image is a subjective matter. The common phrase, â€Å"Beauty is in the eyes of the beholder,† holds true meaning in this sense. One’s

Simple Linear Regression Free Essays

string(661) " 200 300 400 500 600 700 800 900 1000 Appraised Value \(in Thousands of Dollars\) Review: Inference for Regression We can describe the relationship between x and y using a simple linear regression model of the form  µy = \? 0 \+ \? 1 x 1000 900 Sale Price \(in Thousands of Dollars\) 800 700 600 500 400 300 200 100 0 0 100 200 300 400 500 600 700 800 900 1000 Appraised Value \(in Thousands of Dollars\) response variable y : sale price explanatory variable x: appraised value relationship between x and y : linear strong positive We can estimate the simple linear regression model using Least Squares \(LS\) yielding the following LS regression line: y = 20\." Stat 326 – Introduction to Business Statistics II Review – Stat 226 Spring 2013 Stat 326 (Spring 2013) Introduction to Business Statistics II 1 / 47 Stat 326 (Spring 2013) Introduction to Business Statistics II 2 / 47 Review: Inference for Regression Example: Real Estate, Tampa Palms, Florida Goal: Predict sale price of residential property based on the appraised value of the property Data: sale price and total appraised value of 92 residential properties in Tampa Palms, Florida 1000 900 Sale Price (in Thousands of Dollars) 800 700 600 500 400 300 200 100 0 0 100 200 300 400 500 600 700 800 900 1000 Appraised Value (in Thousands of Dollars) Review: Inference for Regression We can describe the relationship between x and y using a simple linear regression model of the form  µy = ? 0 + ? 1 x 1000 900 Sale Price (in Thousands of Dollars) 800 700 600 500 400 300 200 100 0 0 100 200 300 400 500 600 700 800 900 1000 Appraised Value (in Thousands of Dollars) response variable y : sale price explanatory variable x: appraised value relationship between x and y : linear strong positive We can estimate the simple linear regression model using Least Squares (LS) yielding the following LS regression line: y = 20. 94 + 1. 069x Stat 326 (Spring 2013) Introduction to Business Statistics II / 47 Stat 326 (Spring 2013) Introduction to Business Statistics II 4 / 47 Review: Inference for Regression Interpretation of estimated intercept b0 : corresponds to the predicted value of y , i. We will write a custom essay sample on Simple Linear Regression or any similar topic only for you Order Now e. y , when x = 0 Review: Inference for Regression Interpretation of estimated slope b1 : corresponds to the change in y for a unit increase in x: when x increases by 1 unit y will increase by the value of b1 interpretation of b0 is not always meaningful (when x cannot take values close to or equal to zero) here b0 = 20. 94: when a property is appraised at zero value the predicted sales price is $20,940 — meaningful?! Stat 326 (Spring 2013) Introduction to Business Statistics II 5 / 47 b1 0: y decreases as x increases (negative association) b1 0: y increases as x increases (positive association) here b1 = 1. 069: when the appraised value of a property increases by 1 unit, i. e. by $1,000, the predicted sale price will increase by $1,069. Stat 326 (Spring 2013) Introduction to Business Statistics II 6 / 47 Review: Inference for Regression Measuring strength and adequacy of a linear relationship correlation coe? cient r : measure of strength of linear relationship ? 1 ? r ? 1 here: r = 0. 9723 Review: Inference for Regression Population regression line Recall from Stat 226 Population regression line The regression model that we assume to hold true for the entire population is the so-called population regression line where  µy = ? 0 + ? 1 x, coe? cient of determination r 2 : amount of variation in y explained by the ? tted linear model 0 ? r2 ? 1 here: r 2 = (0. 9723)2 = 0. 9453 ? 94. 53% of the variation in the sale price can be explained through the linear relationship between the appraised value (x) and the sale price (y ) Stat 326 (Spring 2013) Introduction to Business Statistics II 7 / 47  µy — average (mean) value of y in population for ? xed value of x ? — population intercept ? 1 — population slope The population regression line could only be obtained if we had information on all individuals in the population. Stat 326 (Spring 2013) Introduction to Business Statistics II 8 / 47 Review: Inference for Regression Based on the population regression line we can fully describe re lationship between x and y up to a random error term ? y = ? 0 + ? 1 x + ? , where ? ? N (0, ? ) Review: Inference for Regression In summary, these are important notations used for SLR: Description x y Parameters ? 0 ? 1  µy ? Stat 326 (Spring 2013) Introduction to Business Statistics II 9 / 47 Stat 326 (Spring 2013) Description Estimates b0 b1 y e Description Introduction to Business Statistics II 10 / 47 Review: Inference for Regression Review: Inference for Regression Validity of predictions Assuming we have a â€Å"good† model, predictions are only valid within the range of x-values used to ? t the LS regression model! Predicting outside the range of x is called extrapolation and should be avoided at all costs as predictions can become unreliable. Why ? t a LS regression model? A â€Å"good† model allows us to make predictions about the behavior of the response variable y for di? rent values of x estimate average sale price ( µy ) for a property appraised at $223,000: x = 223 : y = 20. 94 + 1. 069 ? 223 = 259. 327 ? the average sale price for a property appraised at $223,000 is estimated to be about $259,327 What is a â€Å"good† model? — answer to this question is not straight forward. We can visually check the validity of the ? tted linear model (through residu al plots) as well as make use of numerical values such as r 2 . more on assessing the validity of regression model will follow. 11 / 47 Stat 326 (Spring 2013) Introduction to Business Statistics II 12 / 47 Stat 326 (Spring 2013) Introduction to Business Statistics II Review: Inference for Regression What to look for: Review: Inference for Regression Regression Assumptions residual plot: Assumptions SRS (independence of y -values) linear relationship between x and  µy for each value of x, population of y -values is normally distributed (? ? ? N) r2 : for each value of x, standard deviation of y -values (and of ? ) is ? In order to do inference (con? dence intervals and hypotheses tests), we need the following 4 assumptions to hold: Stat 326 (Spring 2013) Introduction to Business Statistics II 13 / 47 Stat 326 (Spring 2013) Introduction to Business Statistics II 14 / 47 Review: Inference for Regression †SRS Assumption† is hardest to check The †Linearity Assumption† and †Constant SD Assumption† are typically checked visually through a residual plot. Recall: residual = y ? y = y ? (b0 + b1 x) The †Normality Assumption† is checked by assessing whether residuals are approximately normally distributed (use normal quantile plot) plot x versus residuals any pattern indicates violation Review: Inference for Regression Stat 326 (Spring 2013) Introduction to Business Statistics II 15 / 47 Stat 326 (Spring 2013) Introduction to Business Statistics II 16 / 47 Review: Inference for Regression Returning to the Tampa Palms, Florida example: 100 50 Residual 0 -50 -100 -150 0 100 200 300 400 500 600 700 800 900 1000 Review: Inference for Regression Going one step further, excluding the outlier yields 0. 2 0. 1 0. 0 -0. 1 -0. 2 -0. 3 4 4. 5 5 5. 5 log Appraised 6 6. 5 7 Residual Appraised Value (in Thousands of Dollars) Note: non-constant variance can often be stabilized by transforming x, or 0. 5 y , or both: Residual 0. 0 -0. 5 -1. 0 -1. 5 4 4. 5 5 5. 5 log Appraised 6 6. 5 7 outliers/in? uential points in general should only be excluded from an analysis if they can be explained and their exclusion can be justi? ed, e. g. ypo or invalid measurements, etc. excluding outliers always means a loss of information handle outliers with caution may want to compare analyses with and without outliers Stat 326 (Spring 2013) Introduction to Business Statistics II 17 / 47 Stat 326 (Spring 2013) Introduction to Business Statistics II 18 / 47 Review: Inference for Regression normal quantil e plots Tampa Palms example Residuals Sale Price (in Thousands of Dollars) 100 .01 . 05 . 10 . 25 . 50 . 75 . 90 . 95 . 99 Review: Inference for Regression Residuals log Sale 50 Regression Inference Con? dence intervals and hypotheses tests -3 -2 -1 0 1 2 3 Normal Quantile Plot -50 -100 Need to assess whether linear relationship between x and y holds true for entire population. .01 . 05 . 10 . 25 . 50 . 75 . 90 . 95 . 99 Residuals log Sale without outlier 0. 2 0. 1 0 -0. 1 -0. 2 -0. 3 -3 -2 -1 0 1 2 3 This can be accomplished through testing H0 : ? 1 = 0 vs. H0 : ? 1 = 0 based on the estimates slope b1 . For simplicity we will work with the untransformed Tampa Palms data. Normal Quantile Plot Stat 326 (Spring 2013) Introduction to Business Statistics II 19 / 47 Stat 326 (Spring 2013) Introduction to Business Statistics II 20 / 47 Review: Inference for Regression Review: Inference for Regression Example: Find 95% CI for ? 1 for the Tampa Palms data set Con? dence intervals We can construct con? dence intervals (CIs) for ? 1 and ? 0 . General form of a con? dence interval estimate  ± t ? SEestimate , where t ? is the critical value corresponding to the chosen level of con? dence C t ? is based on the t-distribution with n ? 2 degrees of freedom (df) Interpretation: Stat 326 (Spring 2013) Introduction to Business Statistics II 21 / 47 Stat 326 (Spring 2013) Introduction to Business Statistics II 22 / 47 Review: Inference for Regression Review: Inference for Regression Testing for a linear relationship between x and y If we wish to test whether there exists a signi? cant linear relationship between x and y , we need to test H0 : ? 1 = 0 Why? If we fail to reject the null hypothesis (i. e. stick with H0 = ? 1 = 0), the LS regression model reduces to  µy = ? 1 =0 versus Ha : ? 1 = 0 ?0 + ? 1 x ? 0 + 0  · x ? 0 (constant) Introduction to Business Statistics II 24 / 47 = = implying that  µy (and hence y ) is not linearly dependent on x. Stat 326 (Spring 2013) Introduction to Business Statistics II 23 / 47 Stat 326 (Spring 2013) Review: Inference for Regression Review: Inference for Regression Example (Tampa Palms data set): Test at the ? = 0. 05 level of signi? cance for a linear relationship between the appraised value of a property and the sale price Stat 326 (Spring 2013) Introduction to Business Statistics II 25 / 47 Stat 326 (Spring 2013) Introduction to Business Statistics II 26 / 47 Inference about Prediction Why ? t a LS regression model? The purpose of a LS regression model is to 1 Inference about Prediction 2 estimate  µy – average/mean value of y for a given value of x, say x ? e. g. estimate average sale price  µy for all residential property in Tampa Palms appraised at x ? $223,000 predict y – an individual/single future value of the response variable y for a given value of x, say x ? e. g. predict a future sale price of an individual residential property appraised at x ? =$223,000 Keep in mind that we consider predictions for only one value of x at a time. Note, these two tasks are VERY di? erent. Carefully think about the di? erence! Stat 326 (Spring 2013) Introduction to Business Statistics II 27 / 47 Stat 326 (Spring 2013) Introduction to Business Statistics II 28 / 47 Inference about Prediction To estimate  µy and to predict a single future y value for a given level of x = x ? we can use the LS regression line y = b0 + b1 x Simply substitute the desired value of x, say x ? , for x: y = b0 + b1 x ? Inference about Prediction In addition we need to know how much variability is associated with the point estimator. Taking the variability into account provides information about how good and reliable the point estimator really is. That is, which range potentially captures the true (but unknown) parameter value? Recall from 226 ? construction of con? dence intervals Stat 326 (Spring 2013) Introduction to Business Statistics II 29 / 47 Stat 326 (Spring 2013) Introduction to Business Statistics II 0 / 47 Inference about Prediction Much more variability is associated with estimating a single observation than estimating an average — individual observations always vary more than averages!! Inference about Prediction Therefore we distinguish a con? dence interval for the average/mean response  µy and a prediction interval for a single future observation y Both intervals use a t ? critical value from a t-distribution with df = n ? 2. the standard error will be di? erent for each interval: While the point estimator for the average  µy and the future individual value y are the same (namely y = b0 + b1 x ? , the of the two con? dence intervals ! Stat 326 (Spring 2013) Introduction to Business Statistics II 31 / 47 Stat 326 (Spring 2013) Introduction to Business Statistics II 32 / 47 Inference about Prediction Con? dence interval for the average/mean response  µy Width of the con? dence interval is determined using the standard error SE µ (from estimating the mean response) SE µ can be obtained in JMP Keep in mind that every con? dence interval is always constructed for one speci? c given v alue x ? A level C con? dence interval for the average/mean response  µy , when x takes the value x? is given by y  ± t ? SE µ , where SE µ is the standard error for estimating a mean response. Stat 326 (Spring 2013) Introduction to Business Statistics II 33 / 47 Inference about Prediction Prediction interval for a single (future) value y Again, Width of the con? dence interval is determined using the standard error SE µ (from estimating the mean response) SEy can be obtained in JMP Keep in mind that every prediction interval is always constructed for one speci? c given value x ? A level C prediction interval for a single observation y , when x takes the value x ? is given by y  ± t ? SEy , where SEy is the standard error for estimating a single response. Stat 326 (Spring 2013) Introduction to Business Statistics II 34 / 47 Inference about Prediction The larger picture: Inference about Prediction The larger picture cont’d. Stat 326 (Spring 2013) Introduction to Business Statistics II 35 / 47 Stat 326 (Spring 2013) Introduction to Business Statistics II 36 / 47 Inference about Prediction Example: An appliance store runs a 5-month experiment to determine the e? ect of advertising on sales revenue. There are only 5 observations. The scatterplot of the advertising expenditures versus the sales revenues is shown below: Bivariate Fit of Sales Revenues (in Dollars) By Advertising expenditure Inference about Prediction Example cont’d: JMP can draw the con? dence intervals for the mean responses as well as for the predicted values for future observations (prediction intervals). These are called con? dence bands: Bivariate Fit of Sales Revenues (in Dollars) By Advertising expenditure 5000 5000 Sales Revenues (in Dollars) 4000 3000 2000 1000 Sales Revenues (in Dollars) 4000 3000 2000 1000 0 0 0 100 200 300 400 500 600 Advertising expenditure (in Dollars) 0 100 200 300 400 500 600 Advertising expenditure (in Dollars) Linear Fit Linear Fit Sales Revenues (in Dollars) = -100 + 7 Advertising expenditure (in Dollars) Stat 326 (Spring 2013) Introduction to Business Statistics II 37 / 47 Stat 326 (Spring 2013) Introduction to Business Statistics II 38 / 47 Inference about Prediction Inference about Prediction Estimation and prediction (for the appliance store data) Estimation and prediction – Using JMP For each observation in a data set we can get from JMP: y , SEy , and also SE µ . In JMP do: 1 2 We wish to estimate the mean/average revenue of the subpopulation of stores that spent x ? = 200 on advertising. Suppose that we also wish to predict the revenue in a future month when our store spends x ? = 200 on advertising. The point estimate in both situations is the same: y = ? 100 + 7 ? 200 ? 1300 the corresponding standard errors of the mean and of the prediction however are di? erent: SE µ ? 331. 663 SEy ? 690. 411 40 / 47 Choose Fit Model From response icon, choose Save Columns and then choose Predicted Values, Std Error of Predicted, and Std Error of Individual. Stat 326 (Spring 2013) Introduction to Business Statistics II 39 / 47 Stat 326 (Spring 2013) Introduction to Business Statistics II Inference about Prediction Estimation and prediction (cont’d) Note that in the appliance store example, SEy SE µ (690. 411 versus 331. 63). This is true always: we can estimate a mean value for y for a given x ? much more precisely than we can predict the value of a single y for x = x ?. In estimating a mean  µy for x = x ? , the only uncertainty arises because we do not know the true regression line. In predicting a single y for x = x ? , we have two uncertainties: the true regression line plus the expected variability of y -values around the true line. Inference about Prediction Estimation and prediction (cont’d) It always holds that SE µ SEy Therefore a prediction interval for a single future observation y will always be wider than a con? ence interval for the mean response  µy as there is simply more uncertainty in predicting a single value. Stat 326 (Spring 2013) Introduction to Business Statistics II 41 / 47 Stat 326 (Spring 2013) Introduction to Business Statistics II 42 / 47 Inference about Prediction Example cont’d: JMP also calculates con? dence intervals for the mean response  µy as well as prediction intervals for single future observations y. (For instructions follow the handout on JMP commands related to regression CIs and PIs. ) Inference about Prediction Example cont’d: To construct both a con? ence and/or prediction interval, we need to obtain SE µ and SEy in JMP for the value x ? that we are interested in: Month Ad. Expend. S ales Rev. Pred. Sales Rev. StdErr Pred Sales Revenues StdErr Indiv Sales Revenues Let’s construct one 95% CI and PI by hand and see if we can come up with the same results as JMP: In the second month the appliance store spent x = $200 on advertising and observed $1000 in sales revenue, so x = 200 and y = 1000 Using the estimated LS regression line, we predict: y = ? 100 + 7 ? 200 = 1300 Stat 326 (Spring 2013) Introduction to Business Statistics II 43 / 47 Need to ? nd t ? ?rst: Stat 326 (Spring 2013) Introduction to Business Statistics II 44 / 47 Inference about Prediction A 95% CI for the mean response  µy , when x ? = 200: Inference about Prediction A 95% PI for a single future observation of y , when x ? = 200: Stat 326 (Spring 2013) Introduction to Business Statistics II 45 / 47 Stat 326 (Spring 2013) Introduction to Business Statistics II 46 / 47 Inference about Prediction Example cont’d: Advertising exp. Sales Rev. Lower 95% Mean Upper 95% Mean Sales Rev. Sales Rev. Lower 95% Indiv Sales Rev. Upper 95% Indiv Sales Rev. Month Stat 326 (Spring 2013) Introduction to Business Statistics II 47 / 47 How to cite Simple Linear Regression, Papers