W6 bivariate regression

Question 1

Regression and prediction

Answer 1

If there is an association (or correlation) between Variables X and Y

AND

if you know a value on Variable X (e.g., age), then you should be able to use it to make an educated guess about what the corresponding value on variable Y (e.g., cancer risk) will be

Question 2

Predictor and criterion values

Answer 2

in the language of regression,
Variable X would be called the predictor,
and Variable Y the criterion
AND
the predicted value of Y is referred to as Y’ (“y-prime”)
Sometimes referred to as Ŷ (Y-hat)

Question 3

Regression line equation

Answer 3

Y’ = b0 + b1(X1)

Y’  = predicted value of Y
b1 = slope of regression line 
(rate at which Y changes with 
each 1-unit change in X)
b0 = intercept 
(the predicted value of Y when X = 0)

Question 4

Calculating Z scores

Answer 4

(Score - Mean) / Std. Dev.

Question 5

Calculate Sum of Squares

Answer 5

• Calculate the deviation scores (score minus the mean)
• Square the deviation scores
• Sum them up

This part of the process creates a number called the Sums of Squares
Or more fully – the Sums of Squares of deviation scores
-> If I do the extra step of dividing by N I would have the variance. However, in regression we stop at the Sums of squares step

Question 6

Sum of squares and variance types

Answer 6

Total variance: SS for deviation scores from the mean of Y (Y - Y bar)
- referred to as SSY or SSTOT

Systematic variance: SS for deviation of predicted scores from the mean of Y (Y’ - Y bar)
- referred to as SSreg or SSregression

Random variance: SS for deviation of scores from predicted scores
- referred to as SSres OR SSresidual (Y - Y’)

Question 7

R squared

Answer 7

R squared is equal to SSreg divided by SStot

• SSreg and SStot are found in the ANOVA table