correlation coefficient -1 0 1 negative no positive correlation correlation correlation

Correlation Coefficient

-1 0 1

Negative No PositiveCorrelation Correlation Correlation

Correlation Coefficient

-1 0 1

Negative No PositiveCorrelation Correlation Correlation

The closer r, the correlation coefficient, is to 1 or -1, the stronger the relationship.The closer r is to 0, the weaker the correlation (little to no relationship in the data)

-0.9765 is just as strong as 0.9765It just happens to be that -0.9765 is a strong negative correlation and 0.9765 is a strong

positive correlation.

Interpret Correlation Coefficient“Talk about it”

Given the scenario:

Hypothesis: The more students study, the higher the English test scores are.

Data:

Results:a= b=r=

x 1 2 3 4 5

y 72 83 82 94 98


Given the scenario:


Data:

Results:a= 6.3b= 66.9r= 0.962084

x 1 2 3 4 5

y 72 83 82 94 98


Given the scenario:


Data:

Results:a= 6.3b= 66.9r= 0.962084

x 1 2 3 4 5

y 72 83 82 94 98The equation for the line of best fit will

be y = 6.3x + 66.9

r = 0.962084 which is a good correlation coefficient.

It is a Positive Correlation


Given the scenario:

Hypothesis: The more pounds of sand I use, the less pounds of rock I need to fill a patio.

Data:

Results:a= b= r=

x 0 3.5 6.2 11.8 17.3

y 116.1 81.6 43.5 19.8 12


Given the scenario:


Data:

Results:a= -5.963b= 100.88r= - 0.93458

x 0 3.5 6.2 11.8 17.3

y 116.1 81.6 43.5 19.8 12


Given the scenario:


Data:

Results:a= -5.963b= 100.88r= - 0.93458

x 0 3.5 6.2 11.8 17.3

y 116.1 81.6 43.5 19.8 12The equation for the line of best fit will

be y = - 5.963x + 100.88

r = - 0.934584 which is a decent correlation coefficient.

It is a Negative Correlation


Given the scenario:


Data:

Results:a= -5.963b= 100.88r= - 0.93458

x 0 3.5 6.2 11.8 17.3

y 116.1 81.6 43.5 19.8 12The equation for the line of best fit will

be y = - 5.963x + 100.88

r = - 0.934584 which is a decent correlation coefficient.

It is a Negative Correlation

What does the y-intercept tell us?


Given the scenario:


Data:

Results:a= -5.963b= 100.88r= - 0.93458

x 0 3.5 6.2 11.8 17.3

y 116.1 81.6 43.5 19.8 12When x = 0, y = 116.1

Since x represents the pounds of sand and y represents the pounds of rock,

the point (0, 116.1) means when I use 0 pounds of sand I need 116.1 pounds of

rock.



Given the scenario:


Data:

Results:a= -5.963b= 100.88r= - 0.93458

x 0 3.5 6.2 11.8 17.3

y 116.1 81.6 43.5 19.8 12

When x = 0, y = 116.1

Since x represents the pounds of sand and y represents the pounds of rock,

the point (0, 116.1) means when I use 0 pounds of sand I need 116.1 pounds of

rock.


(0, 116.1)


Given the scenario:

Data:

Results:a= -1.417114b= 133.8899r= - 0.36601

x 1 6 15 22 29

y 53 8 125 200 74The equation for the line of best fit will

be y = - 1.417x + 133.89

r = - 0.36601 which is a really close to zero and therefore we can assume

there is no correlation here.