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Name_________________________________ Date: ____________ Lesson 10-2: Correlation Coefficient Learning Goals: #2: What is the correlation coefficient? How do we calculate it and what does it tell us? What is the line of best fit? How do we calculate it and what are its properties? Strength and Direction Strength Direction Linear Regression/The Line of Best Fit: a line in the form ___________________ that fits through the scatterplot of bivariate data. Notation: Facts about the Line of Best Fit: Class Example Use your calculator to determine the equation for the line of best fit. Correlation Coefficient A numerical measurement used to determine the ____________________ and ___________________ of a ______________ relationship. Notation: Facts about r: Class Examples 1) A Math Studies student collected data to determine if there is a correlation between the age of a high school student and the number of hours homework he/she did per week. a) Determine the correlation coefficient. b) What does this tell you about the relationship between age and number of hours of HW? c) Write the equation of the regression line. 2) Matching! Match each scatter plot with the most appopriate correlation coefficient. a) r = -1 b) r = 0 c) r = 1 1) 2) 3) Practice! 4) Estimate the correlation coefficients in each of the following. 5) A statistician wants to know if there is a correlation between PSAT math scores and the Math Studies IB exam scores. She collected the following data from 10 randomly selected students. a) Determine the correlation between PSAT scores and IB Math scores. b) Explain what the correlation tells you in terms of the direction, shape, and strength of the scatterplot that could be used- use context! c) Write the equation of the regression line. 6) For the following, describe the direction, shape, strength, and estimate a correlation coefficient. Direction:________________________________________ Shape:________________________________________ Strength:___________________________________________ Correlation Coefficient:________________ Direction:________________________________________ Shape:________________________________________ Strength:___________________________________________ Correlation Coefficient:________________ Direction:________________________________________ Shape:________________________________________ Strength:___________________________________________ Correlation Coefficient:________________ Direction:________________________________________ Shape:________________________________________ Strength:___________________________________________ Correlation Coefficient:________________ 7) The sketches below represent scatter diagrams for the way in which variables x, y and z change over time, t, in a given chemical experiment. They are labeled 1 , 2 and 3 . x y 1 × × × × ×× ×× × ×× × × × × × time t z 2 × × × × × × × × × × × ×× × × × time t ×× × × × × ×× ×× × ×× × ×× 3 time t (a) State which of the diagrams indicate that the pair of variables (i) is not correlated; (ii) shows strong linear correlation. (b) A student is given a piece of paper with five numbers written on it. She is told that three of these numbers are the product moment correlation coefficients for the three pairs of variables shown above. The five numbers are 0.9, –0.85, –0.20, 0.04, 1.60 (i)For each sketch above state which of these five numbers is the most appropriate value for the correlation coefficient. (ii) For the two remaining numbers, state why you reject them for this experiment.