simple regression

Question 1

regression

Answer 1

-very common for us to attempt to predict variance I an outcome (DV) from one or more predictors (IV)
- aims to tell us: whether our model is a good fir (does it explain a good amount of variance, whether there are significant relationship between a predictor variable and outcome variable and the direction of these relationships

Question 2

R2

Answer 2

• the proportion of total variation (SST) that is explained by the regression (SSR) is known as the coefficient of determination
• often referred to as R2
• this value can range between 0 and 1 and the higher it is the more accurate the regression model is
• it is often referred to as a percentage e.g. R2=.7 means 70% of variance is accounted for

Question 3

adjusted r2

Answer 3

• interpreted in the same way as R2 and is always lower
• an adjustment based on the number of predictors in the model
  -useful because by adding new predictors R2 will inevitably increase

Question 4

model

Answer 4

• R2 and adjusted R2 are used to evaluate model fit
• Whether it is significant or not is determined by an ANOVA (analysis of variance)
• • We get F statistics, degrees of freedom and a p value for the model
  • The F statistic for a regression is calculated using the Mean square for the regression (not the sum of squares of the model SSR) and the mean square of the error (not the sum of squares for the model SSE) –> F= MSR/MSE
  • Degrees of freedom are the number of predictors (k) and N-k-1
    ○ So if I had 100 participants and three predictors my df would be 3,96
    Using the F and the df a p value for the model can be estimated

Question 5

linear regression

Answer 5

• The overall regression model doesn’t tell you information about specific predictors
• you do not know the direction of the association between variables (positive or negative association)
• In order to understand individual predictors it is necessary to look at the individual regression coefficient

Question 6

regression coefficient

Answer 6

• A regression coefficient, B/b, is the number of units the DV changes for each one unit increase in the IV
  ○ B=2.00 means for each unit increase of the IV the DV increases by two units
  ○ B=-.01 means for each one unit increase of the IV the DV decreases by .01 units
• In isolation this value has limited use, and must be interpreted alongside its standard error (SE)
• SE= how much regression coefficient deviates across cases
• Ideally the standard error is small, meaning the regression coefficient is precise
• So logically the larger the regression coefficient is compared to the SE the larger the t statistic will be and the smaller p value calculated for the association

Question 7

standardised regression coefficients

Answer 7

• Beta (β) values are also commonly reported
• They explain the association between each IV and DV in terms of standard deviation changes
  β =.50 means that for every one standard deviation increase in the IV there is a .50 standard deviation increase in the DV
• The most useful property of the beta value is it allows simple comparison of the strength of the association between your Ivs and DV, the higher the beta the stronger the association is
• It is notable that a standardised regression coefficient is just a different way of expressing the same information as an unstandardised regression coefficient so they have exactly the same p value

Question 8

simple and multiple regression assumptions

Answer 8

• Normally distributed continuous outcome
• Independent data i.e. not a within subjects design, data input needs to come from a different participant each time
• Interval/ratio predictors
• Nominal predictors with 2 categories (dichotomous)
• No multicollinearity for multiple regression
• Careful of influencing cases

Question 9

what to do in a simple regression

Answer 9

• load in data
• run the regression
• confidence intervals and beta coefficients

Question 10

full write up

Answer 10

• a simple regression was carried out to investigate the relationship between…
• significant, variance, adjusted r2, f stat and the p value.
  -significance of predictor, b stat, standard error, p value and confidence intervals