Simple Linear Regression

Question 1

What is the difference in the type of research questions, variables and conclusions drawn from correlation vs simple linear regression?

Answer 1

Correlation:
- seeing if a relationship exist between
- two numeric continuous variables

SLR:
- seeing if the DV can be predicted from the IV
- both can be numeric and continuous or you can have one that is numeric and continuous and one that is dichotomous

Question 2

What is the general statistical testing method? (5)

Answer 2

1. Data screening
2. Choosing analysis and preparing data
3. Conducting analyses
4. Understanding and interpreting output
5. Communicating results to target audience

Question 3

In correlation, what is the null hypothesis and what is the alternative hypothesis?

Answer 3

H0: that the population correlation coefficient = 0, ie. That there is no linear relationship

HA: that the population correlation coefficient =/ 0, ie. That there is a linear relationship

Question 4

What tables are there in the output of a SLR statistical analysis? How are they different?

Answer 4

Model as a whole is the first two tables (model summary, ANOVA), coefficients is the last table.

In simple linear regression there is no different between the first two and last table, in multiple regression these are different

Question 5

What values across the model summary tables and coefficients table are the same ONLY FOR SLR?

Answer 5

R^2 (Pearson’s correlation) = B^2 (standardised beta)

P-value from ANOVA table and p-value next to the slope line in coefficients table is the same

t-value^2 from coefficients table is the same as FW

Question 6

What is the null and alternative hypotheses for SLR?

Answer 6

H0: no linear relationship between the predictor, B=0 (slope is 0)

HA: there is a linear relationship between the predictor and outcome variables, B=/0 (slope is not 0)

Question 7

How do you write a conclusion for a correlational analysis?

Answer 7

Write what the correlation is (the two variables) with it’s significance, report r(dfT)=, p=

Eg. maths achievement was significantly higher among students who reported completing more hours of maths homework per week, r(98) = .32, p = .001

Question 8

How do you write a conclusion for SLR?

Answer 8

Report results from the overall regression, R^2=, F(dfB, dfW)=, p=

Report results between the predictor and outcome variable with unstandardised slope, t(dfT)=, p=

Report results between the predictor and outcome variable with standardised slope, t(dfT)=, p=

Question 9

What is multiple linear regression?

Answer 9

Multiple simultaneous independent predictors/variables. Typically, a linear straight line with numeric, continuous variables

Question 10

What is the purpose of MLR? =

Answer 10

To be able to statistically control for different IVs that impact the DV, particularly when we don’t have an experimental design. Allows for the partitioning of variance and the identification of unique relationships

Question 11

What are orthogonal IVs?

Answer 11

Independent variables that are statistically independent to each other (no shared variance)

Question 12

What is the equation for SLR?

Answer 12

Yi = a + bXi + ei

a = alpha = intercept
b = slope coefficient
Xi = score for the ith person
ei = random error for the ith person

Question 13

What is the equation for MLR?

Answer 13

Y(hat)i = a + b1X1i + b2X2i + … (NO error with hat, error when you remove the hat)

a = alpha = intercept
b1 = slope coefficient for IV1
X1i = score for the ith person on IV1

Question 14

What does the R^2 valued mean in MLR?

Answer 14

It is the TOTAL amount of variance in the DV explained by the IV

Question 15

What does the ANOVA table communicate in MLR? What conclusion would you write for this?

Answer 15

It communicates the significance of the overall model as a predictor of the DV.

You say that the model is a significant predictor of the DV, moreso than the null model, F(dfB, dfW)=, p=, R^2 =

Question 16

What does the coefficients table in MLR communicate?

Answer 16

The effects and significance of each predictors on the DV.

It gives the intercept, the slope for each predictor and the significance of each predictor

Question 17

What four components of a MLR do you write in a scientific conclusion?

Answer 17

1. Aim of the study
2. ANOVA F-test
3. Which predictors were significant
4. Conclusions for each significant IV

Question 18

How do you write the conclusions for the IVs in a MLR?

Answer 18

Say how much each increase along X causes an increase in Y (put unstand. beta here) and write what the other IVs are being controlled for, SE=, stand.Beta=, t(dfT)=, p=

Question 19

What three components of a MLR do you write in a plain english conclusion?

Answer 19

1. Aim of the study
2. Trend conclusions for all predictors of interest and significant predictors
3. Take-home message