Chapter 13 finding relationships
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This document contains information about statistics concepts like dependent and independent variables, scatter diagrams, correlation, and regression. It discusses how to interpret a scatter diagram and calculate the correlation coefficient to determine the strength of the linear relationship between two variables. It also explains how to find the line of best fit and use it to make predictions, along with calculating how accurately the line fits the real data using the coefficient of determination. As an example, it analyzes the relationship between marks achieved and time studied, finding a very strong positive correlation between the two variables.
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- 2. 2013/05/23 2 IS THERELATIONSHIPBETWEENVARIABLES STRONGOR WEAK? POSITIVE CORRELATION 0 5 10 15 20 25 30 35 40 0 2 4 6 Y-Values NEGATIVE CORRELATION 0 5 10 15 20 25 0 2 4 6 Y-Values IS THERELATIONSHIPBETWEENVARIABLES STRONGOR WEAK? NO CORRELATION 0 5 10 15 20 25 30 35 0 10 20 30 40 Y-Values NON-LINEAR CORRELATION 0 0.5 1 1.5 2 2.5 3 3.5 0 1 2 3 Y-Values SUMMINGUP CORRELATIONIN A NUMBER • The correlation coefficient 𝑟 is a number that tells us exactly how strong or weak the correlation between two variables is. • Calculate 𝑟 by using the formula: 𝒓 = 𝒙𝒚 − 𝒏𝒙 𝒚 𝒙 𝟐 − 𝒏𝒙 𝟐 𝒚 𝟐 − 𝒏𝒚 𝟐 • Calculate 𝑟 by using your calculator. THE MEANINGOF 𝒓 Perfect Strong Mode- rate Weak No Linear Correlation Weak Mode- rate Strong Perfect -1.00 -0.75 -0.50 -0.25 0.00 +0.25 +0.50 +0.75 +1.00 NEGATIVE CORRELATION POSITIVE CORRELATION CALCULATETHE CORRELATIONCOEFFICIENT: MARKS ACHIEVEDVERSUSTIME STUDIED STUDENT TIME STUDIED (X) IN HOURS MARKS ACHIEVED (Y) IN % A 2 60 B 5 85 C 1 30 D 4 70 E 2 40 SOLUTION 𝒓 = 𝟎. 𝟗𝟑𝟕 Very Strong Positive Linear Relationship
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- 4. 2013/05/23 4 PREDICTINGFROMTHELINE OF “BEST FIT” If your friend only study for 2.5 hours, will he pass the test? 𝒚 = 𝟐𝟏. 𝟓 + 𝟏𝟐. 𝟕𝒙 HOMEWORK •Example X-Kit textbook page 310 – 311. •Practise for your exams page 312 number 1, 2, 3, 4, 5, & 6. •Par B.3 (page B14) all odd number questions.