Unit 3 Section 10-3. 10-3: Correlation  Correlation – statistical method used to determine whether a relationship between variables exists.  The correlation.

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Presentation transcript:

Unit 3 Section 10-3

10-3: Correlation  Correlation – statistical method used to determine whether a relationship between variables exists.  The correlation coefficient is used to determine the strength of the relationship between two variables.  The method we will be using for finding this value is the Pearson product moment correlation coefficient (PPMC).

 Correlation coefficient –measures the strength and direction of a linear relationship between two variables.  Symbol for sample correlation coefficient: r  Symbol for population correlation coefficient: ρ  The values of the correlation coefficient range from -1 to +1.  If the value is close to +1 the variables have a strong positive relationship.  If the value is close to -1 the variables have a strong negative relationship.  If the value is close to 0, the variables have no relationship or a weak relationship. Section 10-3

Formula for the Correlation Coefficient (r) n is the number of data pairs Section 10-3

Constructing a Scatter Plot  Compute the value of the correlation coefficient for the data obtained in the study of age and blood pressure given below: SubjectAge (x)Pressure (y) A43128 B48120 C56135 D61143 E67141 F70152 Section 10-3

Table Set Up: Section 10-3 Subjectxyxyx2x2 y2y2

The correlation coefficient suggested a strong positive relationship between age and blood pressure Section 10-3

Constructing a Scatter Plot  Construct a scatter plot for the data obtained in a study of the number of absences and the final grades of seven randomly selected students from a statistics class. Subject# of Absences (x)Final Grade (y) A682 B286 C1543 D974 E1258 F590 G878 Section 10-3

The correlation coefficient suggested a strong negative relationship between the student’s final grade and the number of absences. i.e. the larger the number of absences, the lower the grade Section 10-3

Constructing a Scatter Plot  Construct a scatter plot for the data obtained in a study on the number of hours that nine people exercise each week and the amount of milk (in ounces) each person consumes per week. SubjectHours (x)Amount (y) A348 B08 C232 D564 E810 F532 G1056 H272 I148 Section 10-3

The value of r indicated a very weak positive relationship between the variables. Section 10-3

Homework:  Read and take notes on Section 10.4 (pg 544 – 554)