Week 9 (Simple Linear Regression II)

Question 1

R squared

Answer 1

The proportion of variance in the outcome variable accounted for by the predictor

Question 2

F-ratio

Answer 2

The ratio of model variance to error variance, whether the regression model is significant.

Question 3

Intercept

Answer 3

The value of the outcome variable when the predictor = 0

Question 4

Slope

Answer 4

The rate of change in the outcome variable in relation the change in the predictor

Question 5

Unstandardised beta (b)

Answer 5

The change in Y for a one unit change in X

Question 6

Standardised beta (β)

Answer 6

The standardised change in Y for one standard deviation change in X

-Another measure of slopes
-B0 (intercept) is always 0
-B1 (the slope): as X increases by one standard deviation, Y changes by B1 of a standard deviation

Question 7

What does an output of Standard Coefficients Beta mean (e.g, -.344)

Answer 7

In this example: As X increases by one standard, Y decreases by .34 standard deviation.

Look at standard deviation readings to see what this means in context

Question 8

When to use standardised OR unstandardised beta

Answer 8

Unstandardised b
-When you want coefficients to refer to meaningful units
-When you want a regression equation to predict values of Y

Standardised β (independent of units)
-When you want an effect size measure, e.g., small/medium/large β is equivalent to small/medium/large r(.1/ .3/ .5)
-When you want to compare the strength of relationship between the predictor and the outcome (across predictors measured in different ways)

Question 9

Covariance

Answer 9

-The extent to which variables co-vary (change together)
-High covariance: means there is a large overlap between the patterns of change (variance) observed in each variable.

Question 10

Outliers influence of regression

Answer 10

-Affect the model’s ability to predict all cases
How influential an outlier is depends on
-Distance between Yobs and Ypred (Residual)
-Leverage (unusual value on predictor)

Cases with standardised residuals or predictors in excess of +- 3.29 (p <0.001) have the potential to be influential outliers

Question 11

How to check for outliers

Answer 11

Standardised residuals (Std. Residual) should have no extreme values (be smaller than 3.29)

Question 12

Assumptions of linear regression

Answer 12

1. Linearity
   -The outcomes (continuous variable) is linearly related to the predictors
2. Independence
   -Observations are randomly and independently chosen from the population
3. Normality of residuals
   -The residuals are normally distributed
4. Homogeneity of variance (homoscedasticity)
   -The variability of the residuals is the same for all levels for the predictors

Question 13

Independence assumption (linear regression)

Answer 13

-This assumption means that the residuals in your model are not related to each other.
-The residuals are NOT independent of each other in cases such as repeated observations on the same subject, or observations from related subjects (e.g twins, students in the same class)
-If this assumption is violated then the model standard errors (SEs) will be invalid, as will the conference intervals (CIs) and significance tests based upon them
-Ensure independent sampling in your design - subjects randomly and independently chosen from the populations.

Question 14

Residual plot

Answer 14

X = ZPRED (standardised predicted value)
Y= ZRESID (standardised residual)

Question 15

Normality assumption (Linear regression)

Answer 15

-The residuals (not IV or DV) should be normally distributed, can be done using histogram and Normal probability plot
-In small samples a lack of normality invalidates confidence intervals and significance tests , whereas in large samples it will not because of the central limit theorem

Question 16

Central limit theorem

Answer 16

The distribution of sample means approximate a normal distribution as the sample size gets larger, regardless of the population’s distribution.

Question 17

The homogeneity of variance assumption

Answer 17

-The variability of the residuals should be the same for all values of Ypred
-Violating this assumption invalidates CIs and significance tests