week 7

Question 1

What is covary

Answer 1

whether two variable covary

Question 2

what does regression do

Answer 2

to predict values of one variable to another

Question 3

How do you find a prediction

Answer 3

finding the regression line

Question 4

What is x-axis

Answer 4

predictor/dependent variable

Question 5

What is Y-axis

Answer 5

Outcome

Question 6

What is simple regression equation

Answer 6

Y=bo+b1x+e

Question 7

what is Y

Answer 7

outcome

Question 8

what is bo

Answer 8

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

Question 9

what is b1

Answer 9

slope of the line: a measure of how much Y changes as X changes, regardless of its sign the larger the value of b1, the steeper the slope. For 1 unit of change on the X axis how much changes is there on the Y axis

Question 10

what is X

Answer 10

predictor

Question 11

what is e

Answer 11

error: residual or prediction error. The difference between the observed value of the outcome variable and what the model predicts

Question 12

What is regression

Answer 12

the line of best fit is. A line that best represents the data, a line that minimises residuals

Question 13

Regression analysis

Answer 13

rather than only looking at relationships, we are interested in making predictions. If we know a participant’s score on X can we predict their value on Y

Question 14

What is the key statistics in regression

Answer 14

R2 value, F value
How the variables relate to each other: The intercept, Beta values: the slope of the regression line

Question 15

Residual sum of squares

Answer 15

residuals can be positive or negative, if we add the residual, 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 residual or residual sum of squares
SSr is a gauge of how well the model fits the data: the smaller SSr, the better fit

Question 16

What is total sum of squares

Answer 16

using the sample mean of observed Y as a baseline model, assuming no relationship between Y and X
The sum of squared difference between the Y and the sample mean total sum of squares
In this baseline model: SSt=SSr.

Question 17

Model sum of squares

Answer 17

Sum of squared difference between the Y and the sample mean

Question 18

SSt= total variance

Answer 18

in the outcome variable can be partitioned into two parts

Question 19

SSr = residual or error variance

Answer 19

variance not explained by the model

Question 20

SSm= model variance

Answer 20

variance explained by the model

Question 21

Regression statistic

Answer 21

R2= SSm/SSt
this provides the proportion of variance accounted for by the model
R2 values range between 0to 1. The higher the value , the better the model interpret r2 as a percentage

Question 22

Regression statistic: F ratio

Answer 22

F=MSm/MSr
F is the ratio of explained variance to the unexplained variance, in other words, F is the ratio of how good the model is compared to how bad it is MSm should be larger than MSr

Question 23

Overall test

Answer 23

The hypothesis in regression can be phrased in various ways
Null hypothesis predicted values of Y are the same regardless of the value of x
Does the model explain significant amount of variance in the outcome variable

Question 24

Coefficients

Answer 24

Characteristics of the regression line: beta values: the slope of the regression line the intercept

Question 25

Unstandardised beta

Answer 25

the value of the slope b1 for every one unit change in x
important to look at whether b1 is positive or negative
if b1 is 0 there is no relationship between X and Y
if a variable significantly predicts an outcome the b-value should be different from zero
This hypothesis is tested using t-test