Linear Correlation Coefficient, r Thus is a measure that shows which - PowerPoint PPT Presentation

D AY 41 – C ORRELATION C OEFFICIENT

V OCABULARY  Scatter Plot - A graph of plotted points that show the relationship between two sets of data.  Positive correlation is a relationship between two variables where if one variable increases, the other one also increases.  Negative correlation is a relationship between two variables such that as the value of one variable increases, the other decreases.

Linear Correlation Coefficient, r Thus is a measure that shows which the extend two variables have a linear relationship. When given two sets of variables, 𝑌 and 𝑍 for which n pairs of measurements (𝑦 𝑗 , 𝑧 𝑗 ) are provided, 𝑗 = 1,2, … 𝑜 , then 𝑜Σ𝑦 𝑗 𝑧 𝑗 − Σ𝑦 𝑗 Σ𝑧 𝑗 𝑠 = 𝑜 Σ𝑦 𝑗 2 − Σ𝑦 𝑗 2 𝑜 Σ𝑧 𝑗 2 − Σ𝑧 𝑗 2 where: n is the total number of pairs of data and r is such that −1 ≤ 𝑠 < 1.

K EY CONCEPT r – is the symbol for correlation coefficient. It measures the direction and strength of a linear association only +1 r -a positive correlation that scatter plot with dots goes up hill ( positive linear regression ) -1r -a negative correlation that scatter plot with dots goes down hill ( negative linear regression )

K EY CONCEPT The association is perfectly linear when r = +1 or r = -1 . The closer to r is to +1 or -1 , the closer the data are to having a perfect linear association.

M ATCH THE GRAPH WITH THE APPROPRIATE C ORRELATION C OEFFICIENT r = 0.094 r = -1.000 r = 0.971

T RY IT YOURSELF r= 1.19 r= -0.002 r= 0.169 r= -0.714

Take a look at your performance in the consecutive mathematics assignments done every day. Consider 15 assignments beginning from the first one is the term going onwards. Or you may as well consider the last term’s consecutive assignments. a). Convert each performance out of 100%.  The formula for determining the percentage 𝑵𝒃𝒔𝒍𝒕 is 𝑼𝒑𝒖𝒃𝒎 𝑵𝒃𝒔𝒍𝒕 × 𝟐𝟏𝟏%  The values should range between 0% and 100%.

b). Make a table of values showing the number of assignments and the performance in each assignment. The table should have two rows or columns where the first one has the number (position of the assignment in the list) of the assignments while the seconds one has the performance out of 100.

c). Generate a scatter plot showing the data above. This should be composed of dots in the positive quadrant of 𝒚𝒛 plane with a line of the best fit.

d).What king correlation does it have? The correlation should be either positive if the student is improving or negative if the students is dropping in performance. There may be no correlation too when the dots are uniformly scattered in the plane.