prediction

when scores on a criterion variable are predicted based on scores from 1 predictor variable, the standardized regression coefficient has _____ value as the correlation coefficient r between the 2 variables. the standardized regression coefficient is ____ value as the correlation coefficient when scores on a criterion variable are predicted based on scores from more than one predictor varaible

-the same -different

in a standardized regression equation, the intercept is always

0

cohen's conventions for R^2 (multiple regression)

0.02 small effect size 0.13 medium effect size 0.26 large effect size

how is the standardized regression coefficient (Beta) for each predictor variable different from r for a multiple regression

Beta will usually be closer to 0 than r bc what makes one predictor successful in predicting the criterion will usually overlap with what makes the other predictors successful in predicting the criterion variable

a=

My-(b)(Mx)

how does the multiple correlation coefficient R usually compare to the sum of all the individual correlations of each predictor with the criterion variable (r1 + r2+ r3...+rn)?

R is usually less than the sum of all the indiv correlations of each predictor with the criterion variable

what is the measure of effect size for multiple regression

R^2 /PRE/ r^2

how to find SStotal of predicted scores

SS(actual-predicted mean)

proportionate reduction in error =

SStotal- SSerror/SStotal

SStotal is equivalent to

SSy

b=

[Sum of (X-Mx)(Y-My)]/SSx

the amount of squared error when predicting without a rule is the

amount of squared error when predicting each score to be the mean

standardized regression coefficient =

b * sqrt(SSx)/Sqrt(SSy)

can you predict using z scores, raw scores, or both?

both (more common to use raw scores)

multiple correlation

correlation of a criterion variable with 2 or more predictor variables

The difference between a person's predicted score on a criterion variable and the person's actual score on that variable is called...

error

a standardized regression coefficient of 0.63 means

for every increase of 1 standard deviation on X, we predict an increase of 0.63 standard deviations on Y

linear prediction rule

formula for predicting a person's score on a criterion variable based on the person's score on one or more predictor variables y-hat= a + b(x) y-hat=predicted score, x=person's score on the predictor variable

the ___ the proportionate reduction in error, the better bc it tells you:

greater, bc it tells you how much less error your X is making in predicting the Y

if we have a small effect size (r^2 is very small), in what way could we still get a stat sig. result

if sample size was very large

multiple correlation coefficient (R)

in multiple regression, the correlation between the criterion variable and all the predictor variables taken together

Proportionate Reduction in Error (r^2 or R^2)

it quantifies the difference that a predictor variable(s) makes in reducing the error in predicting someone's Y, as compared with simply assuming the person's Y will equal the mean of Y.

the standardized correlation coefficient is usually ____ r in multiple regression

less than

limitations on prediction are the same as

limitations for correlation

regression line

line on a graph such as a scatter diagram showing the predicted value of the criterion variable for each value of the predictor variable, shows a linear prediction -slope = regression coefficient (b) intercept= regression constant (a), point at which reg line crosses vertical axis

if 2 variables have 0 correlation, can prediction occur

no

regression coefficient (b)

number multiplied by a person's score on a predictor variable as part of a linear prediction rule -tells you the change in Y for a 1 unit change in X

when does r= beta?

only if a variable is entirely independent and is not correlated with any other IV's in multiple regression -in bivariate regression (simple regression)

regression constant (a)

particular fixed number added into the prediction

bivariate prediction

predicting a person's score on a criterion variable using the person's score on a single predictor variable

multiple regression

procedure for predicting scores on a criterion variable from scores on 2 or more predictor variables

what is the bivariate correlation coefficient

r

the proportionate reduction in error is equivalent to

r^2

the _____ regression coefficient is used to compare a reg coeff from one study with a reg coeff from another study or to compare the size of reg coeff for each of several predictor variables in a multiple regression bc ______ for each variable do not affect it

standardized, different scales

_____ regression coefficients can be less than consistent across diff samples bc they are influenced by the range and variance of the scores in the samples while _____ regression coefficients are not so influenced

standardized, unstandardized

sum of squared errors (SSerror)

sum of the squared differences between each predicted score and actual score on the criterion variable (square bc error can be positive or negative)

error

the difference between a person's predicted score on the criterion variable and the actual score on the criterion variable (Y- Y-hat)

best prediction rule

the line that comes closest to the true scores on the criterion variable aka least squares criterion: smallest sum of squared errors

criterion variable

variable that is predicted (Y)

predictor variable

variable that is used to predict scores of individuals on another variable (usually x)

The PRE or r^2 /R^2 answers the question

what proportion of SStotal is reduced by the regression-produced line?

2 issues in prediction

1. the standardized regression coefficient is needed because the diff scales used to measure the predictor and criterion variables will affect the regular regression coefficient (b) in the linear prediction rule 2. hypothesis testing

assumptions of prediction (4);

1. there is an equal dist of each variable at each point of the other variable 2. the relationship between the variables is linear 3. the cases are independent 4. the error scores are normally distributed

an R^2 of 0.13 tells you that

13% of the overall variation in treatment outcome was predicted by these variables

by least squares criterion, what is our best prediction of y? why?

the mean bc it yields the smallest sum of squared errors in the absence of a predictor

what is the best strategy to take when you cannot use the prediction rule to make a prediction?

the most accurate prediction will be the criterion variable's mean

r tells you

the overall association of the predictor variable with the criterion variable

standardized regression coefficient

the regression coefficient in standard deviation units: its the change in standardized Y for a one SD change in X

prediction rules should only be use for making predictions within

the same range of scores for the predictor variable that were used to come up with the original correlation on which the prediction rule is based

total squared error when predicting from the mean (SStotal)

the sum of squared deviations of Y's from the mean of Y when predicting from the mean, error is =actual score on criterion variable

if variables have larger r's than beta's, this suggests that

the two variables have considerable overlap with each other or other variables in the prediction rule so that their unique contribution to predicting treatment outcome is rather small (beta)

Beta or the standardized regression coefficient tells you

the unique association of this predictor variable, over and above all the other predictor variables, with the criterion variable

As a general rule, Aron et al recommends that unless there is a good reason not to do so, we present _______ in our research reports (talking about regression coefficients)

to include both unstandardized and standardized regression coefficients bc it is hard to define whether a study is purely applied(use unstandardized) or purely theoretical(use standardized)