Linear Regression 2 Flashcards
What tells us how good our linear regression model is?
The error term included in the linear regression equation (+ e).
Of what is the error term included in the regression equation a measure?
Of how spread out the data are around the line of best fit.
How do we find out the numerical values of m and c?
By using the method of least squares.
What is the first step of the linear regression method?
To ascertain the numerical values of m and c.
What is the second step of the linear regression method?
To use the formula Y = mX + c for each of our data points (e.g. X1, X2, etc.) to calculate a set of predicted values (e.g. Y1, Y2, etc.).
What is the third step of the linear regression method?
To calculate the SSR (the sum of squares of residuals which measures the difference between actual data and the model’s predictions).
What is the equation for SSR?
SSR = ∑(Y-Ŷ)2
What is the fourth step of the linear regression method?
To calculate the SST value (the total of the differences between each Y value and the mean Y value).
What is the equation for SST?
SST = ∑(Y-Ȳ)2
In which scenario would SSR be much smaller than SST?
If each actual Y value is much closer to our angled line rather than our flat line.
What indicates that we have a good model (i.e. knowing the value of an independent variable helps us to predict the value of a dependent variable)?
If SSR is much smaller than SST.
The subtraction of which value from SST equals SSM?
SSR
If SSR is much smaller than SST, why would SSM be large?
Because SSM = SST-SSR
What is the ‘goodness of fit’ equation for the linear regression model?
R2 = SSM/ SST
What is the first step involved in carrying out a regression analysis in SPSS?
To select ‘Analyse’- ‘Regression’- ‘Linear’ to fit a straight line.
What is the second step involved in carrying out a regression analysis in SPSS?
To place your dependent variable in the ‘Dependent’ category.
What is the third step involved in carrying out a regression analysis in SPSS?
To place your independent variable(s) in the ‘Independent(s)’ category.
What is the fourth step involved in carrying out a regression analysis in SPSS?
To select ‘Enter’ as your method.
What is the fifth step involved in carrying out a regression analysis in SPSS?
To select ‘Statistics’, then ‘Estimates’ as your regression coefficient, and ‘Model Fit’.
To what does R2 refer?
To the amount of variance in the dependent variable.
How is R2 represented in SPSS?
As ‘R Square’.
Where can SSM be located in a regression output table analysing the overall fit of the model in SPSS?
Underneath ‘Sum of Squares’, and to the right of the ‘Regression’ model.
Where can SST be located in a regression output table analysing the overall fit of the model in SPSS?
Underneath ‘Sum of Squares’, and to the right of the ‘Total’ model.
Where can SSR be located in a regression output table analysing the overall fit of the model in SPSS?
Underneath ‘Sum of Squares’, and to the right of the ‘Residual’ model.
Where can dfM be located in a regression output table analysing the overall fit of the model in SPSS?
Underneath ‘df’, and to the right of the ‘Regression’ model.
Where can dfR be located in a regression output table analysing the overall fit of the model in SPSS?
Underneath ‘df’, and to the right of the ‘Residual’ model.
Where can SSM/ df be located in a regression output table analysing the overall fit of the model in SPSS?
Underneath ‘Mean Square’, and to the right of the ‘Regression’ model.
Where can SSR/ df be located in a regression output table analysing the overall fit of the model in SPSS?
Underneath ‘Mean Square’, and to the right of the ‘Residual’ model.
