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

DAY 41 – CORRELATION COEFFICIENT

VOCABULARY

 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

• ther 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 (𝑦𝑗, 𝑧𝑗) are provided, 𝑗 = 1,2, … 𝑜, then 𝑠 = 𝑜Σ𝑦𝑗𝑧𝑗 − Σ𝑦𝑗Σ𝑧𝑗 𝑜 Σ𝑦𝑗2 − Σ𝑦𝑗 2 𝑜 Σ𝑧𝑗2 − Σ𝑧𝑗 2 where: n is the total number of pairs of data and r is such that −1 ≤ 𝑠 < 1.

KEY 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)

KEY 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.

MATCH THE GRAPH WITH THE

APPROPRIATE CORRELATION COEFFICIENT

r = 0.971 r = 0.094 r = -1.000

TRY IT YOURSELF

r= 0.169 r= 1.19 r= -0.002 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

is

𝑵𝒃𝒔𝒍𝒕 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

• f 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.