week 8

Question 1

Correlations

Answer 1

whether two variables change together or covary
The value of correlation coefficient can vary from -1 to +1

Question 2

Regression

Answer 2

uses correlation to predict values of one variable from another
The prediction is done by finding a regression line that best represents the data

Question 3

X axis

Answer 3

predictor

Question 4

Y axis

Answer 4

outcome

Question 5

regression equation

Answer 5

Y=bo+b1x+e

Question 6

Y

Answer 6

outcome

Question 7

bo

Answer 7

intercept

Question 8

b1

Answer 8

slope of the line

Question 9

X

Answer 9

predictor

Question 10

e

Answer 10

error

Question 11

Intercept

Answer 11

The point at which the regression line crosses the Y-axis
The value of Yi when X=0

Question 12

Slope

Answer 12

a measure of how much Y changes as X changes
Regardless of it’s sign the larger the value of b1, the steeper the slope
For 1 unit of change on the X axis, how much change is there on the Y axis

Question 13

Residual or prediction error

Answer 13

the difference between the observed value of the outcome variable and what the model predicts

Question 14

Lines of best fit

Answer 14

a line that best represents the data
a line that minimises residuals

Question 15

residual sum of squares

Answer 15

residuals can be positive or negative. If we add the residuals, the positive ones will cancel out the negative ones, so we square them before we add them up. We refer to this total as the sum of squared residuals or residual sum of squares
SSr is a gauge of how well the model fits the data

Question 16

Total sum squares

Answer 16

Using the sample mean of observed Y as a baseline model assuming no relationship Y and X
The sum of squared differences between the Yobs and the sample mean total sum squares

Question 17

Model sum of squares

Answer 17

sum of squared differences between the Yobs and the sample mean. It represents the improvement from the baseline model to the regression model

Question 18

SSt

Answer 18

total variance in the outcome variable can be partitioned into two parts

Question 19

SSm

Answer 19

variance explained by the model more variance

Question 20

SSr

Answer 20

variance not experienced by the model residual or error variance

Question 21

R2

Answer 21

this provides the proportion of variance accounted for by the model

Question 22

F ratio

Answer 22

f is the ratio of the explained variance to the unexplained variance

Question 23

Overall test

Answer 23

the hypothesis in regression can be phrased in various ways
can the scores on x and the regression line
does the model explain significant amount of variance in the outcome variable

Question 24

Unstandardised beta

Answer 24

the value of the slope b1
for every one unit change in x, the change in the value of Y. In units of measurement. Important to look at whether b1 is positive or negative
If b1 is 0 there is no relationship between X and Y