EPI/STA 553 Principles of Statistical Inference II Fall 2006 Regression: Testing Assumptions December 4‚ 2006 Linearity The linearity of the regression mean can be examined visually by plots of the residuals against any of the independent variables‚ or against the predicted values. Chart 1 shows a residual plot that reveals no Chart 2 C hart 1 0.4 0.4 0.3 0.3 0.2 0.1 0.1 Residual Residual 0.2 0.0 -0.1 0.0 -0.1 -0.2 -0.2 -0.3 -0.3 -0.4 -0.5
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Regression Analysis Exercises 1- A farmer wanted to find the relationship between the amount of fertilizer used and the yield of corn. He selected seven acres of his land on which he used different amounts of fertilizer to grow corn. The following table gives the amount (in pounds) of fertilizer used and the yield (in bushels) of corn for each of the seven acres. |Fertilizer Used |Yield of Corn | |120
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Types of regression and linear regression equation 1. The term regression was first used as a statistical concept in 1877 by Sir Francis Galton. 2. Regression determines ‘cause and effect’ relationship between variables‚ so it can aid to the decision-making process. 3. It can only indicate how or to what extent variables are associated with each other. 4. There are two types of variables used in regression analysis i.e. The known variable is called as Independent Variable and the variable which
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Topic 8: Multiple Regression Answer a. Scatterplot 120 Game Attendance 100 80 60 40 20 0 0 5‚000 10‚000 15‚000 20‚000 25‚000 Team Win/Loss % There appears to be a positive linear relationship between team win/loss percentage and game attendance. There appears to be a positive linear relationship between opponent win/loss percentage and game attendance. There appears to be a positive linear relationship between games played and game attendance. There does not appear to be any relationship
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Continental Carriers‚ Inc. Advanced Financial Management Continental Carriers‚ Inc. (CCI) should take on the long-term debt to finance the acquisition of Midland Freight‚ Inc. for a few reasons. The company is heavy on assets‚ the debt ratio will only grow to 0.40 with the added $50M in debt. Also‚ the firm will benefit from an added $2M in a tax shield and be able to return $12.7M a year to its stockholders and investors‚ instead of $8.9M if equity is raised to finance the acquisition
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l Regression Analysis Basic Concepts & Methodology 1. Introduction Regression analysis is by far the most popular technique in business and economics for seeking to explain variations in some quantity in terms of variations in other quantities‚ or to develop forecasts of the future based on data from the past. For example‚ suppose we are interested in the monthly sales of retail outlets across the UK. An initial data analysis would summarise the variability in terms of a mean and standard
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Cox Regression Models Questions with Answers Worked Example An investigation is carried out into popularity of new cars being bought in the showroom of a Mercedes dealer. Data recorded for each car included colour‚ engine size and car type. A Cox proportional hazards model was fitted to the data and the results are given below: Write down the Cox hazard function according to this model. With regards to the model you have written down above state the following: • To which class of car does the
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http://www.mathsisfun.com/data/standard-normal-distribution-table.html (Z table) http://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf (t table) Critical Values (Z) Level of Significance 1% 2% 4% 5% 10% Two Tailed ±2.56 ±2.32 ±2.05 ±1.96 ±1.64 Right tailed +2.32 +2.05 +1.75 +1.64 +1.28 Left tailed -2.32 -2.05 -1.75 -1.64 -1.28 Q1) A cinema hall has cold drinks fountain supplying Orange and Ditzy Colas. When the machine is turned on‚ it fills a 550ml cup with 500ml of the
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linear (i.e. if the relationship between y and x is linear). Next perform residual analysis and test for violation of assumptions. (Let y = arterial oxygen and x = blood flow). twoway (scatter y x) (lfit y x) regress y x rvpplot x 2. Since regression diagnostics failed‚ we transform our data. Ratio transformation was used to generate the dependent variable and reciprocal transformation was used to generate the independent variable. 3. Check if the model is adequate by checking the t-statistic
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1. Qeach brand t=β0+β1*PMinute Maid t+β2*PTropicana t+β3*PPrivate label t+ueach brand t Q: quantity P: price By running the above regression model for each brand‚ we got the following elasticity matrix and the figures for “V” and “C.” Note that we used the average price and quantity for P and Q to calculate each brand’s elasticity. Price Elasticity | Tropicana | Minute Maid | Private Label | Tropicana | -3.4620441 | 0.40596537 | 0.392997566 | Minute Maid | 1.8023329 | -4.26820251 | 0.765331803
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