Correlation and Regression

Question 1

Calculating covariance

Answer 1

(∑(x-x̄)(y-ȳ)) / (n-1)

Question 2

Calculating cross product deviations

Answer 2

• calculate the error between the mean and each subject’s score for the first and second variables
• multiply these error values

Question 3

Calculating Correlation coefficient

Answer 3

• convert covariance value to a zscore

- divide through by standard deviation

Question 4

Correlation coefficient

Answer 4

• varies between -1 and +1
• 0 = no relationship
• an effect size

Question 5

Coefficient of determination

Answer 5

r^2

- proportion of variance in one variable shared by the other

Question 6

Direction of causality

Answer 6

correlation coefficients say nothing about which variable causes the other to change

Question 7

The third-variable problem

Answer 7

in any correlation, causality between two variables cannot be assumed because there may be other measures or unmeasured variables affecting the results

Question 8

ANOVA

Answer 8

analysis of variance (ANOVA) is a statistical method used to test differences between two or more means

Question 9

R^2

Answer 9

(ssm)/(sst)
sst = total variability (variability between scores and the means)
ssm = model variability (difference in variability between the model and the mean)

Question 10

F-value

Answer 10

• variation between sample means / variation within the samples
• if your calculated F value in a test is larger than your F statistic, you can reject the null hypothesis

Question 11

Calculating F-value

Answer 11

1. calculate both SDs
2. square both SDs (variance)
3. Divide the largest variance by the smallest variance
4. calculate DFs
5. compare calculated F value to the given value, if the calculated value is larger than the given value then you may reject your null hypothesis

Question 12

Linear regression

Answer 12

• work really well when you have a preponderance of data at the extremes
• the relationship in question may not be linear
• they tell you very little about the biological/biomedical processes at work producing the relationship
• an extension of correlation and a way of predicting the value of one variable from another
• hypothetical model of the relationship between 2 variables
• use equation of a straight line to describe relationship

Question 13

Equation of a straight line for linear regression

Answer 13

y = m(x-a) + b