VCU STAT 210  Lecture16 (59 pages)
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Lecture16
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 59
 School:
 Virginia Commonwealth University
 Course:
 Stat 210  Basic Practice of Statistics
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STAT 210 Lecture 16 Regression Line October 2 2017 Test 3 Friday October 6 Covers chapter 5 pages 99 138 Combination of multiple choice questions and short answer questions and problems Formulas provided please bring calculator and writing instrument Practice Problems Pages 128 through 134 Relevant problems V 2 d V 3 b and d V 4 c and d V 6 b c and d V 7 V 8 b and c V 9 and V 10 Recommended problems V 7 and V 9 Additional Reading and Examples Read pages 120 and 121 Top Hat Motivating Example Students like to make good grades and making good grades is usually associated with studying and learning We will conduct a study to analyze the relationship between time spent studying and grade on a test Describing Relationships We want to use the independent or explanatory variable X to predict the dependent or response variable Y Top Hat Describing Relationships To describe the relationship between two variables we must describe the direction form and strength of the relationship A scatterplot and the correlation coefficient are two statistical tools that can be used to help describe the relationship C Regression Line Now our goal is to determine the equation of the line that best models explains the relationship between X and Y This is referred to as the regression line Equation of a Line Y intercept slope X The intercept is the predicted value of Y when x 0 If x 0 the predicted y is the intercept value The slope is the amount that Y changes increases or decreases when X is increased by one unit If x increases by 1 unit the predicted y increases or decreases by slope units Example 27 slope Sxy Sxx 690 682 5 1 011 This implies that as the number of ads run increases by one ad the predicted number of cars sold increases by 1 011 cars Increases since positive Example 27 intercept y slope x 21 2 1 011 14 5 21 2 14 66 6 54 This implies that if 0 ads are run X 0 then the dealer is predicted to sell 6 54 cars Motivating Example A study is created to evaluate the effect that time spent studying has on the grade earned on a test In this scenario what are the independent X and dependent Y variables X Y Motivating Example A study is created to evaluate the effect that time spent studying has on the graded earned on a test In this scenario what are the independent X and dependent Y variables X time spent studying Y grade on test Motivating Example X time spent studying Y grade on a test Regression line intercept slope Predicted grade on test 36 10 time spent studying Top Hat 2 Prediction We can predict the value of Y for any value of X simply by substituting the value of X into the regression equation Example weight 6 10 age At age 4
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