Week 3- lecture notes (linear model)

Question 1

Terminology for plotting on the x and y axis

Answer 1

y- DV
x- IV

Question 2

slope formula

Answer 2

change in y/ change in x

Question 3

What is an intercept

Answer 3

Predicted Y value for when x is 0

Question 4

How do we calculate what the regression line is

Answer 4

DV=intercept + slope*predictor
-can use this to predict mean of y given a certain value of x (deterministic)

Question 5

Residuals

Answer 5

-regression model doesn’t fit any of the data points perfectly and the amount that it is inaccurate is quantified by residuals
-vertical differences seen coming off the regression line

-add an error term to the regression formula (DV=intercept + weight * predictor + error)
-stidastic- shows that predictions are never going to be perfect

Question 6

What is linear regression

Answer 6

statistical method that’s used to create a linear model

Question 7

What are the 4 different types

Answer 7

• simple linear regression- models using only one predictor
• multiple linear regression- models using multiple predictors
• logistic regression- models a categorical response variable
• multivariate linear regression- models for multiple response variables

Question 8

what are the assumptions of the simple linear regression

Answer 8

-normally distributed (homodasteicity)
-non-constant variance and non-normal residuals don’t follow these assumptions

Question 9

The null model: measuring model fit

Answer 9

-compare normal model with one that only considers the intercept
only calculates as intercept + error term NOT intercept + weight * predictor + error

Question 10

how do we calculate residuals with word frequency model and null model

Answer 10

• do this using sum of squared errors (SSE)
  -null model can be used to create a standardised comparison between the two
  -rsquared = 1-SSEmodel/ SSEnull
  -how much can be accounted for and how much is merely due to chance

Question 11

what does R squared actually measure

Answer 11

-measure of effect size
range from 0-1, values closer to 1 indicate better model fits and stronger effects

-R(squared) uses the residuals of the null model to standardise the residuals of the main model. This provides an effect size and tells us what the proportion of variation in the dependent variable can be accounted for by the predictor in the main model

Question 12

The relationship between fitted values, observed values and residuals can be summarized as follows: residuals = observed values - fitted values

Answer 12

True

Question 13

Statements about R squared that are true

Answer 13

R-squared values range from 0 to 1
R-squared tells us what proportion of variance in the outcome variable can be accounted for by the predictor variables

R-squared is a measure of effect size