Linear Regression 2

Question 1

What tells us how good our linear regression model is?

Answer 1

The error term included in the linear regression equation (+ e).

Question 2

Of what is the error term included in the regression equation a measure?

Answer 2

Of how spread out the data are around the line of best fit.

Question 3

How do we find out the numerical values of m and c?

Answer 3

By using the method of least squares.

Question 4

What is the first step of the linear regression method?

Answer 4

To ascertain the numerical values of m and c.

Question 5

What is the second step of the linear regression method?

Answer 5

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.).

Question 6

What is the third step of the linear regression method?

Answer 6

To calculate the SSR (the sum of squares of residuals which measures the difference between actual data and the model’s predictions).

Question 7

What is the equation for SSR?

Answer 7

SSR = ∑(Y-Ŷ)2

Question 8

What is the fourth step of the linear regression method?

Answer 8

To calculate the SST value (the total of the differences between each Y value and the mean Y value).

Question 9

What is the equation for SST?

Answer 9

SST = ∑(Y-Ȳ)2

Question 10

In which scenario would SSR be much smaller than SST?

Answer 10

If each actual Y value is much closer to our angled line rather than our flat line.

Question 11

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)?

Answer 11

If SSR is much smaller than SST.

Question 12

The subtraction of which value from SST equals SSM?

Answer 12

SSR

Question 13

If SSR is much smaller than SST, why would SSM be large?

Answer 13

Because SSM = SST-SSR

Question 14

What is the ‘goodness of fit’ equation for the linear regression model?

Answer 14

R2 = SSM/ SST

Question 15

What is the first step involved in carrying out a regression analysis in SPSS?

Answer 15

To select ‘Analyse’- ‘Regression’- ‘Linear’ to fit a straight line.

Question 16

What is the second step involved in carrying out a regression analysis in SPSS?

Answer 16

To place your dependent variable in the ‘Dependent’ category.

Question 17

What is the third step involved in carrying out a regression analysis in SPSS?

Answer 17

To place your independent variable(s) in the ‘Independent(s)’ category.

Question 18

What is the fourth step involved in carrying out a regression analysis in SPSS?

Answer 18

To select ‘Enter’ as your method.

Question 19

What is the fifth step involved in carrying out a regression analysis in SPSS?

Answer 19

To select ‘Statistics’, then ‘Estimates’ as your regression coefficient, and ‘Model Fit’.

Question 20

To what does R2 refer?

Answer 20

To the amount of variance in the dependent variable.

Question 21

How is R2 represented in SPSS?

Answer 21

As ‘R Square’.

Question 22

Where can SSM be located in a regression output table analysing the overall fit of the model in SPSS?

Answer 22

Underneath ‘Sum of Squares’, and to the right of the ‘Regression’ model.

Question 23

Where can SST be located in a regression output table analysing the overall fit of the model in SPSS?

Answer 23

Underneath ‘Sum of Squares’, and to the right of the ‘Total’ model.

Question 24

Where can SSR be located in a regression output table analysing the overall fit of the model in SPSS?

Answer 24

Underneath ‘Sum of Squares’, and to the right of the ‘Residual’ model.

Question 25

Where can dfM be located in a regression output table analysing the overall fit of the model in SPSS?

Answer 25

Underneath ‘df’, and to the right of the ‘Regression’ model.

Question 26

Where can dfR be located in a regression output table analysing the overall fit of the model in SPSS?

Answer 26

Underneath ‘df’, and to the right of the ‘Residual’ model.

Question 27

Where can SSM/ df be located in a regression output table analysing the overall fit of the model in SPSS?

Answer 27

Underneath ‘Mean Square’, and to the right of the ‘Regression’ model.

Question 28

Where can SSR/ df be located in a regression output table analysing the overall fit of the model in SPSS?

Answer 28

Underneath ‘Mean Square’, and to the right of the ‘Residual’ model.