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Lesson 4 - R

Lesson 4 - R. Chapter 4 Review. Objectives. Summarize the chapter Define the vocabulary used Complete all objectives Successfully answer any of the review exercises Use the technology to compute required objectives. Problem 1. The scatter diagram below shows a

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Lesson 4 - R

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  1. Lesson 4 - R Chapter 4 Review

  2. Objectives • Summarize the chapter • Define the vocabulary used • Complete all objectives • Successfully answer any of the review exercises • Use the technology to compute required objectives

  3. Problem 1 The scatter diagram below shows a • Moderate positive linear relationship • Weak negative linear relationship • Strong positive linear relationship • Strong nonlinear relationship

  4. Problem 2 The scatter diagram below shows a • Moderate positive linear relationship • Weak negative linear relationship • Strong positive linear relationship • Strong nonlinear relationship

  5. Problem 3 The least squares line below could be • Y = 1.5 X + 1 • Y = – X – 2 • Y = 0.5X – 3 • Y = – 4X + 1

  6. Problem 4 In a study of Y = weight in pounds versus X = age in months of certain dogs, the least squares regression line was found to be Y = 2.7 X + 1.7 The slope has the interpretation • Newborn dogs, on the average, weigh 1.7 pounds • Dogs, on the average, weigh 17 pounds at one year • Newborn dogs, on the average, weight 2.7 pounds • Dogs, on the average, gain 2.7 pounds per month

  7. Problem 5 A coefficient of determination R2 measures • The slope of the least squares regression line • The percent of total variation explained by the least squares regression line • The relationship between the slope and the intercept of the least squares regression line • The size of the residuals of the least squares regression line

  8. Problem 6 The residual plot below shows that • A linear model is inappropriate because of patterns • The correlation is positive • The intercept is negative • A linear model is inappropriate because of slopes

  9. Problem 7 If a linear model is inappropriate because of a pattern in the residuals, one option to try to improve the model is to • Calculate the coefficient of determination • Switch the roles of X and Y • Transform the X or the Y variable • Ignore the residual plot

  10. Problem 8 Using logarithmic transforms to Y and/or to X, we are able to fit which types of models? • Exponential and power • Interquartile range • Positive exponential but not negative exponential • Circular

  11. Summary and Homework • Summary • Summaries of bivariate data • Scatter diagrams • Linear Correlation vs Relationship • Linear models of correlation • Least-squares regression line, y = a + bx • Diagnostics on least-squares regression • Nonlinear models of correlation • Exponential models, y = a + bx • Power models, y = a + xb • Homework • pg 242 – 246; 1, 5, 11-14, 15, 22

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