Vocabulary
The number that determines the strength of the relationship between two variables.
What is the correlation coefficient?
Knowing which of these types your variables fall under is essential for regression, as only the vertical distance is considered.
What is explanatory and response?
This is the residual if the predicted value is 12 and the observed value is 8.
What is 4?
Correlation makes no distinction between these two types of variables.
We found that the coefficient of determination between Tree Height and Amount of Sunlight to be 0.85
85% of the variation in Amount of Sunlight can be explained by the Least Squares Regression Line on Amount of Sunlight based on Tree Height
This type of variable measures the outcome of a study.
What is response?
This value determines the percentage of variation explained by the LSLR.
What is r2?
This is the correlation coefficient r between these points: (1,1); (1,2); (2,3); (3,5); (5,8)
What is 0.9906
The correlation coefficient can only fall between what range?
What is -1 to 1?
We found the correlation coefficient between the Length of a Chalkboard and the Amount of Birthday Cake Eaten to be 0.99998
99.996% of the variation in the Amount of Birthday Cake Eaten can be explained by the Least Squares Regression Line of the Amount of Birthday Cake Eaten based on the Length of a Chalkboard
This type of line of best fit minimizes the squares of distances between points and itself.
What is the Least Squares Regression Line?
A relationship where one variable increases when the other decreases has this type of r value.
What is negative?
This is the Least Squares Regression Line for these points: (4, 6); (7, 8); (9,10); (238,1)
What is ŷ = 8.185 - 0.03x?
r is a number that has none of these associated with it.
What are units?
r2 = 0.47 between Number of Sams in a Class and Average IQ
47% of the variation in the Average IQ can be explained by the Least Squares Regression Line of Average IQ based on Number of Sams in a Class
The formal name of the r2 value.
What is the coefficient of determination?
This point is always on the LSRL.
What is (x̄ , ȳ )?
This is the slope of the Least Squares Regression Line with the following values:
x̄ = 7.1, ȳ = 8.3
Sx = 4.2, Sy = 2.3
r = 0.932
What is 0.510?
It makes no sense for you to use the correlation coefficient r for this type of relationship, no matter how strong it is.
What is non-linear or curved?
r2 = 0.45
x represents the Length of an Eel
y represents the Power of the Electric Shock
45% of the variation in the Power of the Electric Shock can be explained by the Least Squares Regression Line on the Power of the Electric Shock based on the Length of an Eel.
The point with the maximum vertical distance to the Least Squares Regression Line.
What is the regression outlier?
A change in one standard deviation on x corresponds to a change of this many standard deviations on y in the LSRL.
What is r?
This is the full equation for the Least Squares Regression Line with the following values
x̄ = 75.3, ȳ = 14.7
Sx = 8.234, Sy = 5.63
r = 0.2
What is ŷ = 4.4027 + 0.1365x?
Squaring the correlation coefficient gives you this constant.
r = 0.78
x represents the IQ
y represents the Grade Point Average
60.84% of the variation in Grade Point Average can be explained by the Least Squares Regression Line on Grade Point Average based on IQ