Qm - Module 11 - Regression And Correlation

Front 1

Define regression

Back 1

A method for determining the mathematical formula relating the variables

Front 2

Define correlation

Back 2

A method for determining the strength of the relationship between the variables.

Front 3

What are applications for regression analysis?

Back 3

Forecasting

Front 4

Define cross-sectional data

Back 4

the observations relate to different people at one point in time

Front 5

Define time-series data

Back 5

each observation relates to a different point in time

Front 6

When the association between the variables is high with high and low with low, what type of correlation is this called?

Back 6

Positive correlation

Front 7

When the association between the variables is high with low and vice versa, what type of correlation is this?

Back 7

Negative Correlation

Front 8

Define simple linear regression

Back 8

The task of finding the values of a and b which provide the best connection between the two variables.

Front 9

Please explain the meaning of the constants in the equation:
y = a + bx

Back 9

a is the intercept of the y axis

b is the slope of the line

Front 10

A positive slope vs a negative slope - what does that mean for correlation?

Back 10

A positive slope means there is a positive correlation.

A negative slope means there is a negative correlation.

Front 11

Define residual

Back 11

The difference between the actual and fitted values for y.

Front 12

Simple linear regression is the process of

Back 12

deciding which is the best straight line through a set of points, so that the residuals are as small as possible.

Front 13

What possible approaches to deciding which is the best straight line through a set of points?

Back 13

1. Make the best line for which sum of residuals is the least.
2. Make the sum of the absolute values of the residuals as small as possible.
3. (traditional) The least squares method.

Front 14

Define the Least Squares method

Back 14

the sum of the squared residuals is a minimum.

Front 15

How is correlation measured?

Back 15

By calculating the Correlation Coefficient - r. r can take on all values from -1 to +1. Close to -1 or +1 indicate a strong correlation. Close to 0 indicates a weak correlation.

Front 16

Define the explained variation

Back 16

The variation in y that is caused by x.

Front 17

How is explained variation measured?

Back 17

From the difference between the fitted y value and the average y value.

Front 18

What is the essence of correlation?

Back 18

when regression analysis is carried out, the variation in y is split in 2:
a. a part that is 'explained' by associating the y values with the x, and,
b. a part that is unexplained since the relationship is an approximate one and there are residuals

Front 19

What are the general limits for correlation?

Back 19

r > = .75 - highly satisfactory
r = .5 - .75 - adequate
r < .5 - serious doubts

Front 20

What further tests must be made to confirm that the linear equation sufficiently describes the relationship between the variables?

Back 20

1. a visual check of the randomness of the residuals, as plotted on a graph of the linear equation.
2. a scatter diagram of the residuals against the fitted y values

Front 21

List the 4 steps in regression and correlation.

Back 21

1. inspecting the scatter diagram
2. calculating the regression coefficients
3. calculating the correlation coefficients
4. checking the residuals for randomness

Front 22

What is a serial correlation in the residual?

Back 22

Occurs particularly in time-series data where there may be some time-related cycle.

Front 23

Define heteroscedasticity

Back 23

a tendency for residuals to vary in size at different parts of the line. Likely to occur in cross sectional data when the size of residuals is related to the x value.

Front 24

Explain reservations about Regression and Correlation

Back 24

1. Causality - largest source of confusion and error. While association can be determine by analysis, causality cannot be confirmed.
2. Spurious regressions - correlation coefficient is high, but no relationship. Error in setting up model.
3. Extrapolation - should be avoided (using equation outside range of data). Done in forecasting - but must be wary.
4. Regression to single sets of data, when perhaps two lines are more appropriate.
5. Least-squares criterion can be misleading by being too precise.
6. Least-squares has been applied to regressions of y on x.

Front 25

Regression analysis is used ...

Back 25

to include both regression and correlation

Front 26

Forecasting is base on ...

Back 26

regression analysis