Regression

Question 1

What is the general idea of regression?

Answer 1

Data: 2 quantitative variables
Analyze whether there is a relationship between those variables
Check if:
- Positive→move in the same direction
- Negative→move into opposite direction
- No relationship→do not influence each other

Question 2

Analysis of regression

Answer 2

1) Direction
– Positive
– Negative 2) Form
– Linear
– Curve 3) Strength
– Extent of scatter

Question 3

When to use regression?

Answer 3

• Regression line predicts Y value for an X value

* Extrapolation: predicting far outside the X range of our data (should be avoided)

Question 4

For what is the regression line?

Answer 4

Dependent/Response/Explained variable
• on the y-axis
• explained by the variable on the x-axis
Independent/Predictor/Explanatory variable
• on the x-axis
• used to explain the variable on the y-axis

Question 5

Formulas

Answer 5

Regression equation:
y^ = 𝑏 0 + 𝑏 1 𝑥 *
 Slope: tilt of regression line
𝑏1 = 𝑟x( 𝑆𝑦 /𝑆𝑥)
Intercept: Value of Y when X=0
 𝑏0 = 𝑌−𝑏1𝑋

Question 6

What is the least squares regression line?

Answer 6

Line with least errors/that fits best: y^ Minimized distances of the observed y-values from the regression line

Question 7

Need to know about intercept and slope

Answer 7

• Always goes through Point (𝑥ҧ, 𝑦ത)
• Change of 1 standard deviation in X
corresponds to change of r standard
deviations in Y
• Correlation is 0, if slope of line is 0

Question 8

Properties of the least squares regression line

Answer 8

𝑏0: Intercept: Starting point of the line
- When independent variable is equal to 0
𝑏1: Slope of the line
- If we increase our independent variable by 1
unit, the dependent variable will go up by b1
The model selects b0 and b1 in such a way that the sum of the squared residuals* (from the sample) are minimized

Question 9

What is the SSE (error)?

Answer 9

Difference between the observation (y) and the fitted line (𝑦ො)
→ Part we cannot explain “Error = e”
𝑒 = 𝑦 − y^
Formula and graph success formula

Question 10

What is the SSR (Regression)?

Answer 10

Difference between the line (𝑦^) and the mean (𝑦ത) → Difference we can explain