Homework ReviewThe Correlation CoefficientHidden VariablesThe Regression IdentitySums of Squares on the TI-83Explaining VariationThe Coefficient of DeterminationAssignmentCorrelationRobb T.KoetherHomeworkReviewTheCorrelationCoefficientHiddenVariablesTheRegressionIdentitySums ofSquares onthe TI-83ExplainingVariationTheCoefficient ofDeterminationAssignmentCorrelationLecture 50Section 13.7Robb T. KoetherHampden-Sydney CollegeWed, Dec 3, 2008CorrelationRobb T.KoetherHomeworkReviewTheCorrelationCoefficientHiddenVariablesTheRegressionIdentitySums ofSquares onthe TI-83ExplainingVariationTheCoefficient ofDeterminationAssignmentOutline1Homework Review2The Correlation Coefficient3Hidden Variables4The Regression Identity5Sums of Squares on the TI-836Explaining Variation7The Coefficient of Determination8AssignmentCorrelationRobb T.KoetherHomeworkReviewTheCorrelationCoefficientHiddenVariablesTheRegressionIdentitySums ofSquares onthe TI-83ExplainingVariationTheCoefficient ofDeterminationAssignmentHomework ReviewExercise 13.22, page 858.Consider the summaries of the average summertemperature and the corresponding average wintertemperature for the 50 United States.TOTAL OBSERVATIONS: 50SUMMER WINTERN OF CASES 50 50MINIMUM 55.500 10.000MAXIMUM 90.000 72.500MEAN 75.240 33.730STANDARD DEV 5.747 12.995SUMMER WINTERSUMMER 1.000WINTER 0.574 1.000(a) What is the correlation between summer and wintertemperatures?(b) Give the least squares regression equation forregressing y = summer temperature on x = wintertemperature.CorrelationRobb T.KoetherHomeworkReviewTheCorrelationCoefficientHiddenVariablesTheRegressionIdentitySums ofSquares onthe TI-83ExplainingVariationTheCoefficient ofDeterminationAssignmentHomework ReviewSolution(a) The correlation is r = 0.574.(b) For the regression line ... (TBA).CorrelationRobb T.KoetherHomeworkReviewTheCorrelationCoefficientHiddenVariablesTheRegressionIdentitySums ofSquares onthe TI-83ExplainingVariationTheCoefficient ofDeterminationAssignmentThe Correlation CoefficientLetSSX =X(x − x)2,SSY =X(y − y)2,SSXY =X(x − x)(y − y).Then the correlation coefficient isr =SSXY√SSX · SSY.CorrelationRobb T.KoetherHomeworkReviewTheCorrelationCoefficientHiddenVariablesTheRegressionIdentitySums ofSquares onthe TI-83ExplainingVariationTheCoefficient ofDeterminationAssignmentSome CorrelationsFor the Free Lunch vs. Graduation Rate,r = −0.8544.For English SOL Passing Rate vs. Graduation Rate,r = 0.7500.For the Teachers’ Salary vs. Graduation Rate,r = 0.0817.For the S/T Ratio vs. Graduation Rate,r = 0.0022.CorrelationRobb T.KoetherHomeworkReviewTheCorrelationCoefficientHiddenVariablesTheRegressionIdentitySums ofSquares onthe TI-83ExplainingVariationTheCoefficient ofDeterminationAssignmentSome CorrelationsFor the Free Lunch vs. Graduation Rate,r = −0.8544.For English SOL Passing Rate vs. Graduation Rate,r = 0.7500.For the Teachers’ Salary vs. Graduation Rate,r = 0.0817.For the S/T Ratio vs. Graduation Rate,r = 0.0022.CorrelationRobb T.KoetherHomeworkReviewTheCorrelationCoefficientHiddenVariablesTheRegressionIdentitySums ofSquares onthe TI-83ExplainingVariationTheCoefficient ofDeterminationAssignmentSome CorrelationsFor the Free Lunch vs. Graduation Rate,r = −0.8544.For English SOL Passing Rate vs. Graduation Rate,r = 0.7500.For the Teachers’ Salary vs. Graduation Rate,r = 0.0817.For the S/T Ratio vs. Graduation Rate,r = 0.0022.CorrelationRobb T.KoetherHomeworkReviewTheCorrelationCoefficientHiddenVariablesTheRegressionIdentitySums ofSquares onthe TI-83ExplainingVariationTheCoefficient ofDeterminationAssignmentSome CorrelationsFor the Free Lunch vs. Graduation Rate,r = −0.8544.For English SOL Passing Rate vs. Graduation Rate,r = 0.7500.For the Teachers’ Salary vs. Graduation Rate,r = 0.0817.For the S/T Ratio vs. Graduation Rate,r = 0.0022.CorrelationRobb T.KoetherHomeworkReviewTheCorrelationCoefficientHiddenVariablesTheRegressionIdentitySums ofSquares onthe TI-83ExplainingVariationTheCoefficient ofDeterminationAssignmentAnother Formula for rAnother formula for r isr =1(n − 1)Xx − xsxy − ysy.This formula is based on the z-scores of x and y.CorrelationRobb T.KoetherHomeworkReviewTheCorrelationCoefficientHiddenVariablesTheRegressionIdentitySums ofSquares onthe TI-83ExplainingVariationTheCoefficient ofDeterminationAssignmentAnother Formula for rExample (Correlation Coefficient)Height (x) Weight (y )x − xsxy − ysyx − xsxy − ysy70 185 0.0 0.1945 0.000065 140 -1.5 -1.5557 2.333671 180 0.3 0.0000 0.000076 220 1.8 1.5557 2.800368 150 -0.6 -1.1668 0.700167 170 -0.9 -0.3889 0.350068 185 -0.6 0.1945 -0.116772 200 0.6 0.7778 0.466774 210 1.2 1.1668 1.400269 160 -0.3 -0.7778 0.23338.1675CorrelationRobb T.KoetherHomeworkReviewTheCorrelationCoefficientHiddenVariablesTheRegressionIdentitySums ofSquares onthe TI-83ExplainingVariationTheCoefficient ofDeterminationAssignmentAnother Formula for rExample (Correlation Coefficient)Now computer =19(8.1675) = 0.9075.CorrelationRobb T.KoetherHomeworkReviewTheCorrelationCoefficientHiddenVariablesTheRegressionIdentitySums ofSquares onthe TI-83ExplainingVariationTheCoefficient ofDeterminationAssignmentThe Danger of Hidden VariablesSuppose we investigate the relationship in children (3rd- 5th grade) between number of hours spent watchingTV and their reading level.One would expect a negative relationship.CorrelationRobb T.KoetherHomeworkReviewTheCorrelationCoefficientHiddenVariablesTheRegressionIdentitySums ofSquares onthe TI-83ExplainingVariationTheCoefficient ofDeterminationAssignmentThe Danger of Hidden VariablesWeak Positive CorrelationHours watching TVReading levelCorrelationRobb T.KoetherHomeworkReviewTheCorrelationCoefficientHiddenVariablesTheRegressionIdentitySums ofSquares onthe TI-83ExplainingVariationTheCoefficient ofDeterminationAssignmentThe Danger of Hidden VariablesThere appears to be a weak positive relationshipbetween the two variables!What an amazing discovery! Tell the kids to shut thebooks and watch more TV!CorrelationRobb T.KoetherHomeworkReviewTheCorrelationCoefficientHiddenVariablesTheRegressionIdentitySums ofSquares onthe TI-83ExplainingVariationTheCoefficient ofDeterminationAssignmentThe Danger of Hidden VariablesBut now consider a possible third variable: grade level.Divide the sample into three groups according to gradelevel (3rd, 4th, and 5th).CorrelationRobb T.KoetherHomeworkReviewTheCorrelationCoefficientHiddenVariablesTheRegressionIdentitySums ofSquares onthe
View Full Document
Unlocking...