Cronbachs alpha and linear regresssion

What is the difference between correlation and regression

• Correlation looks for symmetric relation between variables

• Correlation assumes bivariate normality

• Regression examines how one or more variables (X) can predict another variable (Y)

• Regression assumes residuals are normally distributed and that the predicting variables are measured without error

How is cronbachs alpha used to measure internal reliability

• Determines the internal consistency or average correlation of items in a questionnaire to measure it’s internal reliability

• Should range between 0 and 1 and shouldn’t be negative

• An alpha > 0.7 is considered good

What do you look for in correlation and regression

Looking for the relation (usually linear) between variables so we can draw a straight line through the data

What is an acceptable value for cronbachs value

• Larger than 0.7

• 0.8 > alpha > 0.7 is acceptable

• 0.9 > alpha > 0.8 is good

What is a residual

The difference between a particular value of Y and itx predicted value

What is a regression line

A line of best fit which accounts for the data we have

What is regression

• A way of predicting the value of one variable from another

• Hypothetical model of the relationship between 2 variables

Equation for regression line

Y = b0 + b i x i

Y- the regression line

b i, gradient of the regression line

Direction/strength of relationship

b 0, intercept, value of Y when X=0

Point at which the regression line crosses the Y axis

How do we calculate the model (the regression line)

• This is a prediction of what we should be able to find

• Fit the model that best describes the data

• This minimises the error in the model

• “Line of best fit”

• Best does not necessarily mean good

How reliable is this regression line model

• The regression line is only a model based on data

• This model may not necessarily reflect reality

How can we test the model

• F test ANOVA

• SSt, total variance in the data

• SSm, improvement due to the model

• SSr, error in the model

• If the model results in better prediction than using the mean, then we expect SSm to be much greater than SSr

• We would want the ANOVA to be significant

How can we test the model using R squared

Can use the proportion of variance accounted for by the regression model

How can we use regression to make predictions

Regression is used to make predictions based on available data

What are outliers

• Exceptional or Atypical values

• We can identify this by examining residuals

• Large residuals means there is a serious mismatch between the observation and prediction

• Any standardised residual larger than 3 is considered too large