Linear Regression

Question 1

Linear Regression

Answer 1

Examine linear relationship between independent/predictor variables and a continuous dependent/outcome variable

Question 2

Simple Linear Regression

Answer 2

1 independent/predictor variable

Question 3

Multiple Linear Regression

Answer 3

> 1 independent/predictor variable

Question 4

Fitted Line (best fit) Equation

Answer 4

Y= b0 + b1X
b0 = intercept
b1 = slope

Question 5

Slope

Answer 5

The average amount of change in the outcome variable for each one-unit increase in the predictor variable
-Characterizes the relationship or marginal effect

Question 6

Residual

Answer 6

Relationship between each individual observation and the trend line can be measured by the vertical distance between each data point and the trend line

Question 7

Residual is also known as what?

Answer 7

Estimated Error (u)

Question 8

Can the residual be negative and positive values?

Answer 8

YES.
Positive = above the trend line
Below = under the trend line

Question 9

What is the Regression Equation mean?

Answer 9

Sum of the fitted line and the error term

Question 10

Sum of Squares Regression

Answer 10

How far the predicted values on the fitted line differ from the overall mean
SSB between on ANOVA

Question 11

Sum of Squares Residual

Answer 11

Difference between the original data and the predicted values on the fitted line
SSW within on ANOVA

Question 12

Residual and Regression Sum of Squares demonstrates what?

Answer 12

Variance

Question 13

For a Regression calculation what must be done first?

Answer 13

ANOVA and F-Stat
-confirm or deny significance prior to proceeding with the rest of the regression calculations

Question 14

ANOVA and F-Stat state whether or not the regression model is significant, but what does it NOT tell us?

Answer 14

1. Positive or Negative Relationship
2. Extent of change in Dependent Variable based on Independent Variable

Question 15

b1 the SLOPE is what?

Answer 15

UNSTANDARDIZED estimate of slop coefficient

Question 16

The t-stat in a regression where the p-value is less than alpha you would what?

Answer 16

REJECT null hypothesis that b=0

Question 17

The 95% CI for a regression cannot include what if you want to reject the null hypothesis?

Answer 17

ZERO

Question 18

b1 the Slope tells you the direction of the relationship (+/-), and extent of change in dependent variable based on independent variable, but it does NOT tell us what?

Answer 18

1. Proportion of variance in dependent variable explained by independent variable

Question 19

Coefficient of Determination

Answer 19

Proportion of the variance in the dependent variable explained by the independent variable

Question 20

R^2 is the Coefficient of Determination (square of Pearson coefficient), and that R^2 value is interpreted how?

Answer 20

R^2 = variance in outcome explained by the exposure

Question 21

1-R^2 = what?

Answer 21

Proportion of variance in outcome NOT explained by exposure

Question 22

R^2 is bounded between 0 and 1 what do the values imply?

Answer 22

1 = excellent model fit
0 = no model fit

Question 23

Adjusted R^2

Answer 23

1. Always lower than R^2
2. Adjusts for inherent increase in R^2 that occurs every time we add an independent variable to regression equation
3. Preferable when comparing models and multiple linear regression

Question 24

Multiple Linear Regression

Answer 24

Examine linear relationships between two or more independent variables and a continuous dependent variable

Question 25

What does Multiple Linear Regression consider?

Answer 25

1. Accounts for Confounders 2. Assess for Moderator effects

Question 26

Multiple Linear Regression does not look at a trend line but what?

Answer 26

Best Fit PLANE

Question 27

The goal is to remove each and every possible source of bias this allow for what?

Answer 27

Estimates to be more unbiased, more efficient, and CLOSER to the true population parameter aka a lower variance

Question 28

What type of outcome variable MUST be utilized in a linear regression?

Answer 28

CONTINUOUS the predictor variables (exposure) do not have to be

Question 29

Continuous Regression Coefficient

Answer 29

All other control variables besides the one being analyzed are held constant and the 95% confidence interval does NOT include 0

Question 30

Binary Regression Coefficient

Answer 30

Dummy variables are BINARY and take a value of 1 if a particular criterion is met and zero otherwise The 95% confidence interval INCLUDES 0

Question 31

Is the Adjusted R^2 preferred or not?

Answer 31

YES, adjusted R^2 adds a penalty for incorporating extra control variables into the model LOWER value due to the penalties

Question 32

Adj R^2 < R^2

Answer 32

A large difference between the two values indicates the possibility of superfluous control variables

Question 33

Manifestation of Effect of a Modified Variable

Answer 33

Should be tested and if statistically significant remain as an independent variable

Question 34

How would you check to see if a Moderator Variable is significantly significant?

Answer 34

Two Way Interaction 1. Forces effects to be additive 2. If the outcome changes/depends on various factors affects the exposure the effects are NOT simply additive but ALSO MULTIPLICATIVE

Question 35

b0 and b1 are what type of predictor variables?

Answer 35

UNSTANDARDIZED Estimates of intercept and slope coefficients

Question 36

What is SE?

Answer 36

Standard Error of the Coefficients

Question 37

What is B?

Answer 37

STANDARDIZED Regression Coefficient in SD UNITS

Question 38

Can you compare between unstandardized and standardized units?

Answer 38

NO

Question 39

t = b-BH0/SE

Answer 39

For a simple linear regression, the t-statistic is the square root of the analysis F statistic

Question 40

Unstandardized b

Answer 40

Relative predictions of unstandardized regression coefficients CANNOT be compared t each other

Question 41

Standardized B

Answer 41

Permit direct comparison of regression coefficients to one another (i.e. which independent variable explained more variance in the dependent variable)

Question 42

What are the Factors that influence appropriateness of Multiple Linear Regression?

Answer 42

1. Homoscedasticity 2. Multicollinearity

Question 43

Homeoscedasticity of Residuals

Answer 43

Variance is the same at ALL points along the regression line

Question 44

If there is homoscedasticity present at a points appearing in a pattern, what type of test should be used instead?

Answer 44

Logistic Regression

Question 45

Multicollinearity

Answer 45

Strong correlations between predictor variables (r> 0.90) =RESULT IN TYPE II ERROR

Question 46

If Multicollinearity is present, what test should be used instead?

Answer 46

Stepwise Regression