week 6 Correlation

Question 1

Correlation

Answer 1

A simple form of relationship between 2 variables. It assesses the degree and direction of a relationship.

A positive correlation is where as the 1st variable increases, so too does the 2nd variable.

A negative correlation is where as the first variable increases, the 2nd variable decreases

Correlations range from -1 to 1. If data is random, correlation approaches or equals zero.

Question 2

Regression

Answer 2

Is an extension of correlation. It allows for the prediction of one variable, based on the scores from another variable.

Question 3

X axis

Answer 3

Typically is for the predictor variable. This variable is the one used to make a prediction for the other variable (Y).

X is usually the independent variable.

Question 4

Y axis

Answer 4

is typically used for the criterion variable

Y is usually the dependent variable.

Question 5

Regression Line

Answer 5

also known as “line of best fit”. Used on a scatterplot. Once have a regression line, are able to make a prediction for Y, given X.

Question 6

Pearson’s Correlation Coefficient (r)

Answer 6

r=COV_xy/S_xS_y

where COV_xy=covariance

S_x=standard deviation of X

S_y= standard deviation of Y.

The null hypothesis states that there is no correlation between the 2 variables, rho (p)=0.

The 2-tailed hypothesis states that rho does not equal zero.

The 1-tailed hypothesis states either rho<0 (negative correlation)or rho>0(positive correlation).

To determine the significance of r, we use a t statistic:

t=r [square root of (N-2)]/square root of (1-r²)

degrees of freedom for this t is N-2.

Note that r=0.75 is considered a strong positive relationship.

r=0 to 0.3 considered small

Question 7

Covariance

Answer 7

this is a number which indicates the degree to which 2 variables vary together.

COV=[Σ(X-X^-)(Y-Y^-)]/N-1

Question 8

r²

Answer 8

r² is the predicted or explained variance. It represents the percentage of variance accounted for in one variable, due to the other variable. So if r=0.75, then r²=0.56=56% of the variability in 1st variable is explained by the 2nd variable.

Question 9

Factors that can affect the Correlation Coefficient

Answer 9

1. If the range is restricted, ie the standard deviation of the variables is very small, then usually (but not always), the magnitude of the correlation is reduced.
2. outliers or extreme data points can have a big impact on the correlation coefficient (reduces it).
3. Heterogenous sub samples. This most commonly occurs when unknowingly the data has 2 subsets (eg male and female) and their combined correlation coefficient may be substantially different than if they each had had a correlation coefficient calculated.