W4: RQ for Predictions 1

Question 1

What is a prediction

Answer 1

Using knowledge about one/more constructs to indicate people’s standing on another construct.

Used in the sense of indication (not explanation or cause)
e.g. a barometer predicts, but does not explain/cause the weather

Question 2

What is in a good RQ involving prediciton

Answer 2

1. ) Statement ending with ?
2. ) Include all relevant constructs
3. ) Indicate all relevant population
4. ) Use predict as “driving word” (key)

Question 3

DV/IV in a prediction RQ. X/Y. Does the meaning and focus of RQ change if X and Y swapped?

Answer 3

DV: Being Predicted - Y Variable
IV: Predictor - X Variable.

it changes depending on which variable is defined on the DV/IV.

Question 4

What is “Variation”. How is it measured

Answer 4

Variation:

Total amount of variability in a distribution of scores from the mean.

Measured:

Sum of squared deviation scores (or Sum of Squares). Gets larger as n increases

Question 5

What is “Variance”. How is it measured

Answer 5

Variance:

AVERAGE Sum of Squares in a distribution of scores (both population and samples)

Measured:

Expressed in a squared metric, relative to the scores on which it is calculated

Question 6

What is “Standard Deviation”. How is it measured

Answer 6

Standard Deviation:

Square Root of Variance (both population and samples)

Measured:

Expressed in same metric as scores on which it is calculated

Question 7

What is the key distinguishing features between correlation and regression

Answer 7

Correlation: Symmetric Relationship
Regression: Asymmetric Relationship

Question 8

What is a Symmetric Relationship. In terms of correlation; IV/DV; scatterplot

Answer 8

Variables have the SAME role and function in the characteristic of scores being summarised.

Cor (A,B) = Cor (B,A)
No IV/DV
Scatterplot: Variable on X/Y axis does not matter

Question 9

What is a Asymmetric Relationship. In terms of correlation; IV/DV; scatterplot

Answer 9

Variables have the DIFF role and function in the characteristic of scores being summarised.

Cor (A,B) /=/ Cor (B,A)
IV/DV declared priori
Scatterplot: Variable on X/Y axis fundementally important

Question 10

What is the conceptual formulation of a correlation

Answer 10

Sum of all the cross product of z-scores / df

> STANDARDIZED (conversion to z) measure of strength and direction of association

Question 11

What is the conceptual formulation of a covariance

Answer 11

Sum of all the cross product of deviation scores/ df

> UNSTANDARDIZED (using deviation) measure of strength and direction of association

Question 12

Can we calculate correlation from covariance, vice versa?

Answer 12

Yes

Question 13

What is the line of best fit

Answer 13

Linear Regression Line

Question 14

What is the slope value of a regression line: Formulation

Answer 14

Correlation (xy) x (SDy / SDx)

Question 15

What is bx (slope value of a regression line) and an estimate of

Answer 15

It is a sample statistic and also an estimate of the corresponding population parameter

Question 16

How can the slope value be interpreted as

Answer 16

For any 1 unit increase on the X variable, the value of Y variable increases (b) units

Question 17

What is the full regression equation

Answer 17

Yi = a + bXi + ei

Yi = observed scores on DV
Xi = observed scores on IV
ei = residual scores (difference between observed and predicted scores ON DV)
a = intercept

Question 18

What is the regression model equation

Answer 18

Y^i = a + bXi

Y^i = predicted scores on DV
Xi = observed scores on DV
a = intercept
b = regression coefficient (expected change in scores on DV for each unit change of IV)

Question 19

In a regression equation, what does a^ and b^ aim to do.

Answer 19

By using Ordinary Least Squares Estimator (OLS)

a^ and b^ aims to MINIMIZE the sum of squared residuals (i.e. Max strength of prediction)

Question 20

What is the difference between simple and multiple linear regression model

Answer 20

Simple:
- One intercept + One regression coefficient
Yi = a + bXi + ei

Multiple:
- One intercept + p partial independent variables (where p >= 2)

Yi = a + b1X1i + … + bpXpi + ei

Question 21

What is the aim in research using linear regression

Answer 21

Use sample regression estimates to make an inference about corresponding unknown population parameter values

Question 22

In R Studio, in a linear regression. Where the IV/DV and what are the properties

Answer 22

DV is always on the left. Must be numeric

IV is always on the right. Either numeric/factor

Question 23

Are the coefficient value for each value in simple regression the same as the coefficient value in the multiple regression. Explain.

Answer 23

Different.

In a multiple regression, the correlation AMONG IVs in their relationship to DV is partialled out/removed.
> Slope of each edge is an effect that is INDEPENDENT of the other DV

Question 24

What is the interpretation of the intercept in a regression model

Answer 24

Predicted value on the DV when people have a zero on all independent variable in the model

Question 25

What is the upper and lower bound in a 95% confidence interval

Answer 25

2.5% and 97.5%

Question 26

How do we interpret a 95% confidence interval of 0.10 and 0.86

Answer 26

We can be 95% confidence that the population coefficient value for the regression of ____ on ___ is between 0.10 and 0.86

Question 27

What is an unbiased 95% confidence interval

Answer 27

Over a large number of repeated samples drawn from the population, the confidence interval calculated in each sample will contain the true population parameter value 95% of the time on average

i.e. actual converge rate will be 95% over the long run

Question 28

What if the interval estimator is biased

Answer 28

Actual converge rate will be smaller/larger than the nominal rate OVER THE LONG RUN (e.g. 89%/98%)

Question 29

What if the interval estimator is consistent

Answer 29

Actual converge rate will get INCREASINGLY closer to 95% over the long run as sample size increases