Topic 11 B: Regression

Question 1

What is a regression line used for?

Answer 1

To perdict the value of y for a given value of x
Ex: How fast do alchol sales rise with a one unit increase in amount of subliminal exposure?

Question 2

After verifying that a correlation is significant, you can —–

Answer 2

determine the equation of the line that best fits the data

Question 3

Residuals

Answer 3

The difference between th eobserved y-value and the predicted y-value for a given x-value on a line

Question 4

Positive residual

Answer 4

Underestimated outcome

Question 5

Negative residual

Answer 5

Overestimated outcome

Question 6

What is a regression line?

Answer 6

The line for which the sum of the squares of the residuals is a minimum.

Question 7

The regression line always passes through the point:

Answer 7

Question 8

Two types of variation about a regression line:

Answer 8

• explained variation (due to variable x)
• Unexplained variation (Due to unknown factors)

Question 9

Coefficient of Determination

Answer 9

• The ratio of the explained variation to the total variation
• Denoted R^2

Question 10

What does r^2 value of 0.833 mean?

Answer 10

Question 11

The standard error of estimate

Answer 11

• The standard deviation of the observed yi-values about the predicted y-values for a given xi-value

Question 12

The closer the observed y-values are to the predicted y-values, the —– the SE of estimate will be

Answer 12

smaller

Question 13

Simple regression vs correlation + ex

Answer 13

Simple regression is predicting values on one variable using info from one predictor variable. (Given a particular sense of humour rating, what attractiveness rating would we expect a person to receive?)
Correlation is describing strength and direction of relationship between 2 variables (how much does y go up with an increase with X and also considering maybe increase/decrease in another variable length)

Question 14

Multiple regression +ex

Answer 14

Predicting values on an outcome variable from values on more than one predictor variable. Ex: A more accurate prediction of perceived attractiveness might be made if we considered facial symmetry and intelligence.

Question 15

Why conduct multiple regression (3)?

Answer 15

• Can quantify combined effects of more than 1 variable (ex: how much of the variance in attractiveness is accounted for by sense of humor and facial symmetry?)
• Allows us to examine the relative influence of different predictor variables (is sense of humor, facial symmetry or intelligence more important in determining a person’s attractiveness?)
• Can quantify and describe interaction relationship between predictor variables ( does sense of humour affect attractiveness rating only when facial symmetry is low?

Question 16

Multiple regression equation:

Answer 16

Use UNSTANDARDIZED COEFFICIENTS

Question 17

Assumption of multiple regression (3)

Answer 17

1. Linearity between each of the predictors and the criterion (outcome variables)
2. Residuals are normally distributed (about zero), there is no clustering
3. No extreme multicollinearity (cant have predictors that are highly correlated) No +/- 0.8 or bigger in abs value

Question 18

R is the

Answer 18

correlation between one variable (Y) and a set of predictors

Question 19

Running SPSS multiple regression anaylses to determine whether all 3 predictors combined can significantly predict overall rating above chance:

Answer 19

F-statistics

Question 20

Sun SPSS multiple regression anaylses to determine whether each predictor variable significantly contributes to the prediction of overall rating on its own:

Answer 20

t-test

Question 21

Run SPSS multiple regression anaylses to determine the relative contibution of each predictor variable to overall evaluation scores

Answer 21

compare standardized betas