Simple -> Multiple Regression

Question 1

SIMPLE REGRESSION

Answer 1

R^2 - GOODNESS OF FIT
- for simple regression, R^2 = square of correlation coefficient
- reflects variance accounted for in data by best fit line
- takes values between 0 (0%)/1 (100%)
- frequently expressed as percentage > decimal
- high values show good fit; low values show poor fit

Question 2

LOW R^2 VALUES

Answer 2

• R^2 = 0
• 0% = randomly scattered points; no clear relation between X/Y
• implies that a bets-fit line will be v poor description of data
• aka. good best fit line = high proportion of variance explained

Question 3

HIGH R^2 VALUES

Answer 3

• R^2 = 1 (impossible!)
• 100% = points lie directly on line; perfect relation between X/Y
• implies best fit line = v good description of data
• aka. moderate best fit line = less variance explained

Question 4

HIGH R^2 VALUES

Answer 4

• R^2 = 1 (impossible!)
• 100% = points lie directly on line; perfect relation between X/Y
• implies best fit line = v good description of data

Question 5

SIGNIFICANCE TESTS

Answer 5

• reported in SPSS output
  SIMPLE REGRESSION
• t-test; established if model describes statsig proportion of variance in data
  MULTIPLE REGRESSION
• uses ANOVA to discover if proportion of variance in data explained by model = statsig

Question 6

MULTIPLE REGRESSION

Answer 6

R^2 - GOODNESS OF FIT
- R^2 will get larger every time another IV (regressor/predictor) is added to model
- new regressors may only provide small improvement in amount of variance in data explained by model
- need to establish “added value” of each additional regressor in predicting DV

Question 7

EFFECTIVENESS (VS EFFICIENCY)

Answer 7

• all possible contributory causes (IVs); maximises R^2
• explains largest possible proportion of variance in DV/outcome
• maximises R^2 (ie. maximises proportion of variance explained by model)

Question 8

EFFICIENCY (VS EFFICTIVENESS)

Answer 8

• only includes most important variables (IVs)
• gives largest step increase in R^2ADJ
• maximises increase in R^2ADJ upon adding another regressor (ie. if new regressor doesn’t add much to variance explained it isn’t worth adding)

Question 9

EFFECTIVENESS SCALE

Answer 9

0-25%
- v poor; likely unacceptable
25-50%
- poor BUT may be acceptable
50-75%
- good
75-90%
- very good
90%
- likely there’s something wrong w/analysis

Question 10

ARE REGRESSORS STATIG ASSOCIATED W/DV?

Answer 10

• ANOVA test checks if model (as whole) has statsig relation w/DV
• part of predictive value of each regressor may be shared by 1/+ of other regressors in model
• aka. model must be considered as whole (ie. all IVs together)
• read off ANOVA table in SPSS output; report as in ANOVA (ie. F (3,12) = 4.33; p = .028)

Question 11

INDIVIDUAL REGRESSORS x DV

Answer 11

• SPSS output entitled COEFFICIENTS
• column headed “un-standardised coefficients - B” gives regression coefficient for each regressor variable (IV)
• units of coefficient = same as for regressor (IV)
• all other variables must be held CONSTANT

Question 12

REGRESSOR W/GREATEST EFFECT ON DV

Answer 12

• units for each regression coefficient = dif aka. we must standardise them to compare
• column headed “standardised coefficients - beta”
• can compare beta weights for each regressor variable to compare effects of each of DVs
• larger beta weight indicates stronger effect of regressor on DV values

Question 13

ARE REGRESSOR RELATIONS W/DV STATSIG?

Answer 13

• assessed using t-test
• check values in column headed t/sig
• if regression coefficient = negative -> t-value will also be negative (doesn’t matter about sign; t size = important)