10. REGRESSION

Question 1

1. What is Linear Regression?

Answer 1

• this is another statistical technique
• it is used for assessing the association between 2
  numeric variables

Question 2

2. What does Linear Regression Assess?

Answer 2

• it assesses the extent to which an increase in one
  variable is associated with an increase in the other
  variable

Question 3

3. What does Linear Regression go hand in hand with?

Answer 3

• it goes hand in hand with correlation
• the 2 techniques complement each other
• they help to give a complete picture of the association
  between 2 numeric variables

Question 4

4. How does Linear Regression Operate?

Answer 4

• it operates by fitting a line-of-best-fit in a scatter plot
• it does this using the least-squares method
• you would use the line that best describe the data
• this is the line that runs through the most point dots

Question 5

5. What does “Best Fit” mean?

Answer 5

• this is when the overall difference between the actual
  (observed) Y values
  AND the predicted Y values is at a minimum

Question 6

6. Does this diagram of the Line of Best Fit make sense?

Answer 6

• yes

Question 7

7. What is the Line of Best Fit formula for any given association between 2 numeric variables?

Answer 7

• Y’ = a + bX

Question 8

8. What does the Y’ stand for?

Answer 8

• this is the predicted value of Y
• this value is predicted by X

Question 9

9. What does the b stand for?

Answer 9

• this is known as Beta
• this is the slope of the line
• it represents the Regression Coefficient

Question 10

10. What does the a stand for?

Answer 10

• this is known as Alpha
• this is the Y-Intercept

Question 11

11. What is the Regression Coefficient?

Answer 11

• this represents the estimated change in the Y variable
  for each 1 unit increase in the X variable
• the change in the Y variable can be an increase or a
  decrease

Question 12

12. Does this example of the Regression Coefficient make sense?

Answer 12

• yes

Question 13

13. What can be interpreted from this graph?

Answer 13

• the Y-Intercept is at 0.30
• the Regression Coefficient is -0.22
• this means that the Y value will decrease by 0.22 units
  for every 1 unit increase in the X value

Question 14

14. What is the necessary question to ask ourselves when it comes to the Correlation Coefficient?

Answer 14

• how strong is the association

Question 15

15. What is the necessary question to ask ourselves when it comes to the Regression Coefficient?

Answer 15

• how much does a change in X predict a change in Y