MATH CHAPTER 4
Linear correlation
how closely the points of a scatter diagram closely approximate a straight line pattern
Positive correlation
a relationship between two variables in which both variables either increase or decrease together
Regression Line Formula
y^1 = a + bx
Number of hours practicing golf and golf score
Negative linear correlation
Number of hours practicing bowling and bowling score
Positive linear correlation
Temperature outside and ice cream sales
Positive linear correlation
The coefficient of correlation between x and y is r = 0.59. Calculate the coefficient of determination R?
0.59^2 = 0.35 r^2 = 035
Correlation
A measure of strength relationship between two variables
Amount of alcohol consumed and reaction time
Positive linear correlation
Amount of grams of fat consumed daily and cholesterol level
Positive linear correlation
The speed of a vehicle and the time the vehicle reaches its destination
Negative linear correlation
A person's weight and the value of his/her home
No linear correlation
Mother's birth weight and her child's birth weight
No linear correlation
If r = 0?
No linear relationship exists between the variables
R = 0
Non linear relationship
R= -1
Perfect negative
R=1
Perfect positive
R = -0.9
Strong negative
R= 0.91
Strong positive
In the NHL the correlation between "goals scored per game" and "minutes on the ice" for a team of players is found to be 0.8178. Choose the statement that is true about the coefficient of determination
The coefficient of determination r^2 is equal to approximately 0.668. When given as a percent the coefficient of determination is always between 0 and 100% The coefficient of determination states that about 66.88% of the variation in goals scored per gram is explained by minutes on the ice.
How do you interpret a coefficient of determination; r^2 equal to 0.95?
The interpretation is that 95% of the variation in the dependent variable can be explained by the variation in the independent variable.
Correlation coefficient can be zero?
The statement is true.
What does it mean to say that the linear correlation between two variables equals 1? What would the scatter diagram look like?
When the linear correlation coefficient is 1 perfect positive linear reaction between two variables. The scatter diagram would contain points that all lie on a line with a positive slope.
Scatter diagram
a graph representing the ordered pairs of data on a set of axes
Regression
is a statistical technique that produces a model of the relationship (correlation) between the two variables
Coefficient of determination (r^2)
measures the proportion of the variance of the dependent variable y that can be accounted for by the variance of the independent variable x. calculated by squaring the correlation coefficient, r and making it r^2
No linear correlation
no linear relationship between the two variables. The high and low measurements for the two variables are not associated in any predictable straight line pattern
Value r = 0
represents no linear correlation
Value r= -1
represents the strongest negative linear correlation
Value r=1
represents the strongest positive linear correlation
y^1
the predicted value of y (the dependent variable) given the value of x (the independent variable)
a AND b
the regression coefficients
Negative Correlation
the relationship between two variables in which one variable increases as the other variable decreases
The coefficient of determination is _____ of the linear correlation coefficient
the square
Pearson's correlation coefficient (r)
the strength of a linear correlation between the two variables can be numerically measured by Pearson's r