Correlation Robb T Koether Homework Review Correlation The Correlation Coefficient Lecture 50 Section 13 7 Hidden Variables The Regression Identity Robb T Koether Sums of Squares on the TI 83 Hampden Sydney College Explaining Variation Wed Dec 3 2008 The Coefficient of Determination Assignment Outline Correlation Robb T Koether 1 Homework Review Homework Review 2 The Correlation Coefficient The Correlation Coefficient 3 Hidden Variables Hidden Variables 4 The Regression Identity The Regression Identity 5 Sums of Squares on the TI 83 Sums of Squares on the TI 83 6 Explaining Variation Explaining Variation 7 The Coefficient of Determination 8 Assignment The Coefficient of Determination Assignment Homework Review Correlation Robb T Koether Homework Review The Correlation Coefficient Hidden Variables The Regression Identity Sums of Squares on the TI 83 Explaining Variation The Coefficient of Determination Assignment Exercise 13 22 page 858 Consider the summaries of the average summer temperature and the corresponding average winter temperature for the 50 United States TOTAL OBSERVATIONS N OF CASES MINIMUM MAXIMUM MEAN STANDARD DEV 50 SUMMER 50 55 500 90 000 75 240 5 747 WINTER 50 10 000 72 500 33 730 12 995 SUMMER WINTER SUMMER 1 000 0 574 WINTER 1 000 a What is the correlation between summer and winter temperatures b Give the least squares regression equation for regressing y summer temperature on x winter temperature Homework Review Correlation Robb T Koether Homework Review The Correlation Coefficient Hidden Variables The Regression Identity Sums of Squares on the TI 83 Explaining Variation The Coefficient of Determination Assignment Solution a The correlation is r 0 574 b For the regression line TBA The Correlation Coefficient Correlation Robb T Koether Homework Review The Correlation Coefficient Hidden Variables The Regression Identity Sums of Squares on the TI 83 Explaining Variation The Coefficient of Determination Assignment Let SSX X x x 2 SSY X y y 2 SSXY X x x y y Then the correlation coefficient is r SSXY SSX SSY Some Correlations Correlation Robb T Koether Homework Review The Correlation Coefficient Hidden Variables The Regression Identity Sums of Squares on the TI 83 Explaining Variation The Coefficient of Determination Assignment For 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 Some Correlations Correlation Robb T Koether Homework Review The Correlation Coefficient Hidden Variables The Regression Identity Sums of Squares on the TI 83 Explaining Variation The Coefficient of Determination Assignment For 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 Some Correlations Correlation Robb T Koether Homework Review The Correlation Coefficient Hidden Variables The Regression Identity Sums of Squares on the TI 83 Explaining Variation The Coefficient of Determination Assignment For 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 Some Correlations Correlation Robb T Koether Homework Review The Correlation Coefficient Hidden Variables The Regression Identity Sums of Squares on the TI 83 Explaining Variation The Coefficient of Determination Assignment For 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 Another Formula for r Correlation Robb T Koether Homework Review The Correlation Coefficient Hidden Variables The Regression Identity Sums of Squares on the TI 83 Explaining Variation The Coefficient of Determination Assignment Another formula for r is X 1 r n 1 x x sx y y sy This formula is based on the z scores of x and y Another Formula for r Correlation Robb T Koether Homework Review The Correlation Coefficient Hidden Variables The Regression Identity Sums of Squares on the TI 83 Explaining Variation The Coefficient of Determination Assignment Example Correlation Coefficient Height x Weight y 70 65 71 76 68 67 68 72 74 69 185 140 180 220 150 170 185 200 210 160 x x sx 0 0 1 5 0 3 1 8 0 6 0 9 0 6 0 6 1 2 0 3 y y sy 0 1945 1 5557 0 0000 1 5557 1 1668 0 3889 0 1945 0 7778 1 1668 0 7778 x x sx y y sy 0 0000 2 3336 0 0000 2 8003 0 7001 0 3500 0 1167 0 4667 1 4002 0 2333 8 1675 Another Formula for r Correlation Robb T Koether Homework Review The Correlation Coefficient Hidden Variables The Regression Identity Sums of Squares on the TI 83 Explaining Variation The Coefficient of Determination Assignment Example Correlation Coefficient Now compute 1 r 8 1675 0 9075 9 The Danger of Hidden Variables Correlation Robb T Koether Homework Review The Correlation Coefficient Hidden Variables The Regression Identity Sums of Squares on the TI 83 Explaining Variation The Coefficient of Determination Assignment Suppose we investigate the relationship in children 3rd 5th grade between number of hours spent watching TV and their reading level One would expect a negative relationship The Danger of Hidden Variables Correlation Robb T Koether Weak Positive Correlation Homework Review Hidden Variables The Regression Identity Reading level The Correlation Coefficient Sums of Squares on the TI 83 Explaining Variation The Coefficient of Determination Assignment Hours watching TV The Danger of Hidden Variables Correlation Robb T Koether Homework Review The Correlation Coefficient Hidden Variables The Regression Identity Sums of Squares on the TI 83 Explaining Variation The Coefficient of Determination Assignment There appears to be a weak positive relationship between the two variables What an amazing discovery Tell the kids to shut the books and watch more TV The Danger of Hidden Variables Correlation Robb T Koether Homework Review The Correlation Coefficient Hidden Variables The Regression Identity Sums of Squares on the TI 83 Explaining Variation The Coefficient of Determination Assignment But now consider a possible third variable grade level Divide the sample into three groups according to grade level 3rd 4th and 5th The Danger of Hidden Variables Weak Positive Correlation Correlation Robb T Koether Homework
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