L18 - Regression 2

Question 1

what are the two types of models and how do they differ?

Answer 1

deterministic models have no randomness within them
probabilistic models have randomness
both describe the relationship between variables.

Question 2

describe what a deterministic model is and provide an example.

Answer 2

They hypothesise the exact relationship between two variables. they are suitable when prediction error is negligible.
- an example is a linear graph of distance and time to produce speed.

Question 3

Describe a Probabilistic model and provide an example.

Answer 3

probabilistic models hypothesise two components
- deterministic
- Random error
Example: Income varies among based on education level.

Question 4

within the line of best fit regression model what does B1 represent?

Answer 4

B1 estimates the amount of change in Y given by a change of 1 in X. (AKA the slope )

Question 5

within the line of best fit regression model what does B0 represent?

Answer 5

B0 represents the value of Y given that the value of X is zero (AKA the Y-intercept)

Question 6

what are the four cautions of regression?

Answer 6

• Spurious relationships
• Extrapolation
• Generalisation
• Causation

Question 7

what is a Spurious correlation in Regressions? and why is it a problem?

Answer 7

This occurs when the mathematical relationship between the two variables are not actually directly linked and have no relationship.

Question 8

what is Extrapolation in terms of a regression model? and why is it a problem?

Answer 8

Extrapolation occurs when inference about the line of best fit is made outside where the data-points lie. this can be a problem because the relationship between the variables could change with higher and lower values of X.

Question 9

what is Generalisation in a regression model? why can it be a problem?

Answer 9

generalisation occurs when a conclusion is drawn from a small dataset and applied to a larger population. This can be a problem because the sample may not accurately represent the population.

Question 10

what is an Outlier? and why can it be a problem within a regression analysis ?

Answer 10

outliers are data points that are significantly different from the other data points within a sample. They can be a problem because they can skew the line of best fit and reduce correlation r^2 values

Question 11

what is an Influential point within a dataset?

Answer 11

it is a point that significantly affects the line of best fit.

Question 12

how does the removal of an influential point within a dataset affect the line of best fit?

Answer 12

it changes the slope of the line (B1)

Question 13

Are all influential points outliers?

Answer 13

no