Lesson 4 - R

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