W4: RQ for Predictions 1

Question 1

Predictions: What is it, and what is the keyword? What does it not do?

Answer 1

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

• Indicate / Account for / Explain (if used descriptively)
• Not cause
  
  • Barometer indicates / account for /explain (if used descriptively), but it does not 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: Y-Axis
  
  • Being Predicted (Predicted)
• IV: X-Axis
  
  • Doing the predicting (Predictor)
• Meaning and focus of RQ change 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
  
  • Sum of squared deviation scores; or
  • Sum of squares
    
    • Hence, gets larger as n increases

Question 5

What is “Variance”. How is it measured and expressed

Answer 5

Variance

• Average Sum of Squares in a distribution of scores
• Expressed in a squared metric, relative to the scores on which it is calculated
  
  • Hence, it is independent of sample size

Question 6

What is “Standard Deviation”. How is it expressed

Answer 6

Standard Deviation

• Square Root of Variance
• Expressed in same metric as scores on which it is calculated

Question 7

What is the geometrical interpretation of deviations

Answer 7

• SD
  
  • Length
• Variance
  
  • Area (It is a square)
• Variation
  
  • Sum of all the Areas/Squares
  • (That’s why it’s called sum of squares)

Question 8

What is the key distinguishing features between correlation and regression

Answer 8

• Correlation
  
  • Symmetric Relationship
• Regression
  
  • Asymmetric Relationship

Question 9

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

Answer 9

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 10

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

Answer 10

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

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

Question 11

What is the formula and conceptual formulation of a correlation

Answer 11

Correlation

• Sum of cross products of deviation z-scores / (n-1)
• r_xy = E (Z_xi x Z_yi) / n - 1
  
  • Standardised (z) measure of strength and direction of association
  • (X and Y deviations in z will not be the same!)
• We can look at the size of correlation to determine the strength of the association directly (-1 to 1)

Question 12

What is the conceptual formulation of a covariance

Answer 12

Covariance

• Sum of cross product of deviation scores / (n-1)
• S_xy = E [(X_i - μ_x ) x (Y_i - μy)] / (n-1)
  
  • Unstandardised (using deviation) measure of strength and direction of association
  • (X and Y deviations will not be the same!)
• We cannot look at the size of covariance to determine the strength of the association directly (-∞ to +∞)

Question 13

Can we calculate correlation from covariance, vice versa? In what circumstances can we do that

Answer 13

Yes.

But we have to know the standard deviations of variable x and y

• r_xy = S_xy / sd_x x sd_y
• S_xy = r_xy x sd_x x sd_y

Question 14

What alternative name of line of best fit. What does it do?

Answer 14

Linear Regression Line

• Summarise relationship between 2 variables

Question 15

Formula to calculate the slope of the regression line

Answer 15

b_x = r_xy x (SD_y / SD_x)

• Sample correlation x Respective standard deviations.
  
  • Know value of sample correlation
  • Know respective standard deviations
• Therefore, slope will be the same if SD is the same, which is not very possible.

Alternatively,

b = (Y₂ - Y₁ ) / (X₂ - X₁)

Question 16

What is b_x ? An SS or a PP?

Answer 16

• b_x
  
  • Sample statistic
  • An estimate of the population parameter ρ_x
    
    • Don’t forget, population parameter can never be “Calculated”

Question 17

How can the slope value interpreted

Answer 17

• For any 1 unit increase on the X variable
• The value of Y variable increases ____ units

Question 18

What is the full regression equation

Answer 18

• Y_i = a + bX_i + e_i
  
  • Y_i
    
    • _​Observed scores on DV
  • Xi
    
    • Observed scores on IV
  • e_i
    
    • Residual scores
    • Difference between observed and predicted scores on DV
  • a
    
    • Intercept

Question 19

What is the regression model equation

Answer 19

Y^_i = a + bX_i

• Y^i
  
  • Predicted scores on DV
• X_i
  
  • Observed scores on DV
• a
  
  • Intercept
• b
  
  • Regression coefficient
  • Expected change in scores on DV for each unit change of IV

Question 20

What is the SS in linear regression?

Answer 20

SS_total =

• SS_reg
  
  • _​Derived from SS value from Linear Regression Line to Mean
  • I.e. variation explained by linear regression model
• SS_res
  
  • _​Derived from SS value from Linear Regression Line to observed scores
  • i.e. variation not explained by linear regression model

Question 21

In a regression equation, what does a^ and b^ aim to do. What method is this. Is it biased?

Answer 21

Ordinary least squares estimator

• Find values of a^ and b^ to minimise the sum of squared residuals
  
  • Minimise the difference between obsered and predicted values of DV
  • Therefore, Maximize strength of prediction
• OLS is unbiased :)

Question 22

What is the difference between simple and multiple linear regression model

Answer 22

Simple

• One intercept and One regression coefficient
• Y_i = a + bX_i + e_i

Multiple

• One intercept and p partial regression coefficients (where p >= 2)
• Yi = a + b₁X_1i + … + b_pX_pi + e_i

Question 23

What is the aim in research using linear regression

Answer 23

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

Question 24

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

Answer 24

Different

• Multiple regression
  
  • Correlation among IVs in their relationship to DV and with each other is partialled out/removed.
    
    • i.e. if there is no correlations among IVs, simple regression = multiple regression
  • Slope of each edge (partial regression coefficient) is an effect that indepedent of other IVs

Question 25

What is the interpretation of the intercept in a regression model

Answer 25

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

Question 26

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

Answer 26

2.5% and 97.5%

Question 27

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

Answer 27

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

Question 28

What is an unbiased 95% interval estimator. What is it NOT

Answer 28

• Over large number of repeated samples drawn from the population, CIs 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)

NOT 95% chance the population parameter will be captured in an interval

Question 29

What if the interval estimator is biased

Answer 29

Actual converge rate will be smaller/larger than the nominal rate over the long run (e.g. 89%/98%)

Question 30

What if the interval estimator is consistent

Answer 30

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

(If it is 98% and goes to 99% as n increases, it is still not consistent!)