KIN 3502 - Correlation and Prediction

what is correlation?

A measure of relationship between two variables

what is correlation coefficient?

Denoted by r; an index of the linear relationship between two variables, which includes the magnitude and direction of the relationship

True or False: Correlations can only have values that range from -1 to +1?

true

which correlation is most likely to describe the proposed situation: there is a strong relationship between higher levels of physical activity and a decreased risk of death.

r=0.80

What correlation does this show?

r=0.00

what kind of relationship does this show?

strong relationships

what kind of relationship does this show?

weak relationships

What is the relationship between cups of coffee Dr Hulteen drinks and his level of productivity? (r=0.24)

low correlation

what kind of relationship does this show?

no correlation/relationship

what is value?

how good the correlation is

what does the score of 0 mean?

means that there’s no relationship

true or false: correlation has no units

true

what does positive correlation mean?

Participants above the mean on one variable, are more likely to be above the mean on second variable

what does negative correlation mean?

Participants above the mean on first various, are more likely to be below the mean on the second variable

what kind of relationship does this represent: Higher body weight related to low pull-ups / Lower body weight related to higher pull-ups

negative correlation

what does more data give us?

MORE confidence that what we find isn’t a fluke

what is Coefficient of Determination (r²)?

Proportion of shared variance between two measures

what is this an example of?

Coefficient of Determination (r²)

what does a ven diagram mean for coefficient of determination?

Middle portion is shared variance; Individual ends are error (non-shared variance)

what does this mean: distance run x V0_2 Max (r=0.90) (r²=0.81)

81% of variation in V0₂ Max can be predicted by Distance Run and 19% of variation is either error OR can be explained by another variable

what is a curvilinear relationship?

An association among variables that can best be depicted by a curve

true or false: Pearson-product moment coefficients (i.e., correlation) is NOT the best analysis technique for curvilinear relationships

true

true or false: correlation equals causation

false

true or false: correlation are about relationships, not cause and effect

true

true or false: even if relationship is +/- 1.00 other variables could be the cause

true

what is the effect of variance on?

the magnitude of r

True or false: value of r in dots is smaller than value of r in squares

true

what is prediction?

Estimating the value of one variable from one or more variables; X predicts Y to some degree

what is this an example of: To what extent does childhood motor skill competence predict physical activity in adulthood?

prediction

true or false: prediction does imply causation?

false

what is the formula for a straight line?

Ŷ = bX + c

what is this an example of?

straight line

what is simple linear prediction (regression)?

Statistical method used to predict the criterion, outcome, or dependent variable (Y) from a single predictor or independent variable X

what can we do if two variables are correlated?

we can compute a prediction equation

what is the Independent variable (X)?

the variable manipulated or controlled

what is this an example of: treatment; stretching duration and temperature

independent variable (X)

what is the Dependent variable (Y)?

the variable being tested and measured; “Dependent” on the independent variable

what is this an example of: sit-and-reach or ice cream sales

dependent variable (Y)

true or false: it is possible that the dependent variable could cause a change in the independent variable

false

what is multiple regression?

A more complex prediction of Y can be developed with the use of more than one predictor: X₁, X₂ and so on

what is the formula for multiple regression?

Ŷ = b₁X₁ + b₂X₂ + b₃X₃ + … b_nX_n + c

what does E (error) represent?

the inaccuracy of our prediction of Y based on the prediction equation

true or false: Ŷ will not necessarily equal Y

true

what is the formula used for the inaccuracies of a prediction?

Ŷ = bX + c + e

what is the formula for error?

E = Y − Ŷ

if error can be minimized, out prediction becomes more _____

accurate

true or false: error can represent pure measure of a trait when predictor is removed

true

true or false: error cannot indicate lack of fit (i.e., X does not predict Y)

false

what are the Standard Error of Estimate (SEE)?

Standard Error (SE) & Standard Error of Prediction (SEP); Reflects the average amount of error in predicting Y from X ; Standard deviation of error or residual scores

what formula is this for?

standard error

what does S_y stand for?

Standard deviation of Y scores

what does r² stand for?

Coefficient of determination