Psych Stats - Exam 2: Ch. 8

Front 1

what is a linear regression line

Back 1

the line that summarizes a scatterplot by, on average, passing through the center of the Y scores at each X

-- the best fitting straight line

Front 2

what is the linear regression procedure used for

Back 2

to predict Y scores based on the scores from a correlated X

Front 3

what is Y' and how do you obtain it

Back 3

Y' = Y prime = the predicted Y score for a given X; computed from the regression equation

Front 4

general form of a linear regression equation

Back 4

Y' = bX + a

Front 5

what does the Y intercept indicate

Back 5

the value of Y when the regression line crosses the Y axis (X = 0)

Front 6

what does the slope indicate

Back 6

the direction and degree that the regression line is slanted

Front 7

distinguish between the PREDICTOR variable and the CRITERION variable in linear regression

Back 7

X = predictor variable = the given X variable

Y = criterion variable = the to-be-predicted Y variable

Front 8

what is Sy'

Back 8

the standard error of the estimate

Front 9

what does Sy' tell you about the spread in the Y scores

Back 9

it is a standard deviation, indicating the "average" amount that the Y scores deviate from their corresponding vales of Y'

Front 10

why does Sy' tell you about your errors in predicition

Back 10

indicates the average amount that the actual scores differ from the predicted Y' scores, so it is the "average" error

Front 11

in order for the standard error of the estimate to accurate, there are 2 assumptions:

Back 11

assumes Y scores are:

1) homoscedastic -- scores are equally spread out around the regression line at each X

2) normally distributed -- forming a normal distribution around the regression line at each X

Front 12

how does heteroscedasticity lead to an inaccurate description of the data?

Back 12

heterscedasticity means Y scores are not spread out from Y' to the same extent at all Xs, so the standard error of the estimate will over/under-estimate the error, depending on the value of X

Front 13

how is the value of Sy' related to the size of r

Back 13

Sy' is inversely related to the absolute value of r, because the smaller Sy' indicates the Y scores are closer to the regression line (and Y') at each X, which is what happens with a stronger relationship (a larger r)

Front 14

when are multiple regression procedures used

Back 14

when more than one predictor variable (X variable) is correlated with and used to predict the scores on one criterion variable (Y variable)

Front 15

what are 2 statistical names for r^2

Back 15

1) the coefficient of determination

2) the proportion of variance in Y that is accounted for by the relationship with X

Front 16

how do you interpret r^2

Back 16

indicates the proportional improvement in accuracy when using the relationship with X to predict Y scores, compared to using the overall mean of Y to predict Y scores

Front 17

regression analysis is used when:

Back 17

we have 2 variables and they are correlated

uses the correlation between 2 variables to predict unknown or future scores

Front 18

the mean is the best predictor when...

Back 18

we only have ONE variable and we want to predict an unknown score on that variable

--avg amount of error in prediction = standard deviation for that variable

Front 19

accuracy of prediction ENTIRELY depends on

Back 19

the correlation of your two variables

the close r is to +1 or -1, the greater the level of prediction

Front 20

error in prediction

Back 20

the distance from each real data point (y) to the predicted value (y')

best fitting regression line = smallest amount of total error

Front 21

the strong the r (correlation), the _______ the error in prediction

Back 21

smaller

Front 22

2 elements describe the regression line

Back 22

1) slope

2) y-intercept

Front 23

if r = 0, your standard error of estimate = ?

Back 23

the standard deviation of that variable

(this is no better than the mean)

Front 24

assumptions of linear regression

(when its ok to perform linear regression)

Back 24

1) linearity -- there is a linear relationship between variables

2) homoscedasticity -- occurs when Y scores are spread out to the same degree at every X

3) Y scores at each X form an approximately normal distribution

Front 25

when we do NOT use the relationship to predict score

Back 25

--use over mean of Y scores as everyone's predicted Y

--error is Y - (mean of Y)

error is Sy^2

Front 26

when we DO use the relationship to predict scores

Back 26

use the corresponding Y' as determined in by the linear regression equation as our predicted Y value

--error is (Y-Y')

error is Sy^2

Front 27

proportion of variance accounted for is....

Back 27

the proportional improvement in accuracy when using the relationship with X to predict Y, compared to using (mean of Y) to predict Y

Front 28

how is proportion of variance accounted for computed

Back 28

find r^2

"the coefficient of determination"