Correlation & Regression

Question 1

Correlation

Answer 1

A correlation exists between two variables (eg 2 random variables X and Y) if one of them is related to the other in some way.

Question 2

Correlation values

Answer 2

> 0 if X and Y both increase

Question 3

Correlation does not imply what? Why?

Answer 3

Cause-effect relationship, because of the possible existence of a lurking variable.

Question 4

Regression model

Answer 4

A regression model is a mathematical equation that describes the relationship between 2 or more variables.

Question 5

Simple Regression

Answer 5

2 variables

Question 6

Multiple regression

Answer 6

More than 2 variables

Question 7

The 2 variables in a simple regression

Answer 7

Independent and dependent variables

Question 8

Dependent variable

Answer 8

the one being explained

Question 9

Independent variable

Answer 9

The one used to explain the dependent variable.

Question 10

Linear regression

Answer 10

A regression that gives a straight-line r elationship between 2 variables.

Question 11

We use which method to get the best-fitting line?

Answer 11

Method of least squares

Question 12

Method of least squares

Answer 12

We minimize the sum of squares of the distance between the observed values and predicted values for y or x.

Question 13

Always want regression line to do what?

Answer 13

Go through (xbar, ybar)&raquo_space;> ybar = b0+b1 * xbar

Question 14

Sign of b1 depends on

Answer 14

Sxy

Question 15

We cannot use the slope b1 to predict the strength of the relationship because…

Answer 15

it is affected by units.

Question 16

Solution to problem of units

Answer 16

We use a standardized slope, the (Pearson) Linear Correlation Coefficient

Question 17

r has the same sign as…

Answer 17

b1

Question 18

interpreting r

Answer 18

the closer r is to plus or minus 1, the stronger the linear relationship

Question 19

r>0

Answer 19

positive linear correlation

Question 20

r

Answer 20

negative linear correlation

Question 21

r stays the same even if you do what?

Answer 21

change units of x and y or change the role of x and y

Question 22

No significant linear correlation equals

Answer 22

nothing. Does not mean that there is no relation at all

Question 23

When to use the regression line to make predictions

Answer 23

When there is a significant linear correlation

Question 24

Both r and r^2 do what? How are they different?

Answer 24

They both measure the strength of the linear association, but have different interpretations.