2. Multiple Regression

Question 1

What is multiple regression?

Answer 1

Multiple Predictors (likely to correlate) = Finds optimal prediction of the outcome from several predictors (takes into account redundancy with one another)

Question 2

What is multiple regression used for?

Answer 2

Prediction (leads to improved prediction)

Theory Testing (Theories often suggest multiple variables)

Covariate Control (If we want to assess the effect of a specific predictor + controlling the influence of others)

Question 3

How would we interpret the intercept in multiple regression?

Answer 3

Predicted value for y when x are all 0

Question 4

How would we interpret a coefficient in multiple regression?

Answer 4

Change in y for one unit change in x, when all other x’s remain constant

Question 5

What does ‘holding constant’ mean?

Answer 5

Holding effect of x2
Controlling for difference in x2
Partialling out effects for x2
Holding X2 equal
Accounting for effects x2

Can identify the unique contribution of predictors as it means finding effect of predictor when other predictions are fixed

Question 6

What are model predicted values and how do they help us?

Answer 6

Model predicted values are the predictions based on the the data/predicted from regression analysis

Can be compared to actual value (obtained by observation) - the difference being the residual

Question 7

What are marginal distributions and how do we use them?

Answer 7

Distribution of each variable without reference to values of other variables (independent of one another)

Plot each variable individually via density plot and histogram

Numerically explore via summary stats (e.g. mean, SD)

Question 8

What are bivariate associations and what are they used for?

Answer 8

Describes the relationship between two numeric variables

Plot associations among two variables

Numerically explore by reporting correlation

Question 9

Fill in the blank:

The values of the intercept and slope that _______ are our estimated coefficients from our data

Answer 9

Minimise the sum of square residuals

Question 10

How do you calculate the intercept?

Answer 10

Predicted B0 = Mean of y - predicted mean of x

Question 11

How do you calculate the slope?

Answer 11

Sum of cross products/Sum of square deviations

sum(xi - mean x)(yi - mean of y)

divided by

sum(xi (individual PPT) - mean of x) squared