module 10

Question 1

Association between 2 numerical variables, controlling for a categorical variable

Answer 1

Can use scatterplot

Question 2

Association between 2 numerical variables - controlling for a numerical variable

Answer 2

Can use scatterplot

Question 3

Association between a numerical and categorical variable - controlling for another categorical variable

Answer 3

Can plot a side by side boxplot/violinplot visualization

Question 4

Simple OLS regression model:

Answer 4

yhat (response variable) = intercept + slope*explanatory variable

Question 5

Reference/baseline level

Answer 5

a categorical explanatory variable that is not assigned an indicator variable (indicator variable is 0/1)

Question 6

interpreting a numerical variable slope in a multiple linear regression model

Answer 6

“All else held equal, by increasing the given explanatory variable by 1, we expect the predicted response variable to increase/decrease by NUMBER on average.”

Question 7

Formal definition of the indicator variable slope

Answer 7

“All else held equal, we expect the predicted response variable value that corresponds to the given indicator variable level to be NUMBER higher/lower than the reference level, on average”

Question 8

Formal def of the intercept

Answer 8

“We expect the predicted response variable value that corresponds to the observation in which all explanatory and indicator variable values are 0 to be our intercept value, on average.”

Question 9

When to use interaction terms

Answer 9

If you observe diff slopes between a given numerical explanatory variable and the response variable for different levels

Question 10

residual

Answer 10

actual - predicted

Question 11

training dataset

Answer 11

to train the machine learning model; usually 80%

Question 12

Test dataset

Answer 12

to test the machine learning model that has been fit with the training dataset; may calculate the RMSE of the test dataset

Question 13

RMSE

Answer 13

The avg error of each response variable in the dataset; we would have no model error for any of our observations; RMSE = 0, the closer the RMSE to 0, the better

Question 14

SSE

Answer 14

Sum square error (SSE): minimal value of the model; amount of response variable variability in the dataset that is not explained by the model

Question 15

SST

Answer 15

Sum square total (SST): the total amount of response variable variability in the dataset

Question 16

SSR

Answer 16

Sum square regression (SSR) = SST - SSE; Amt of response variable variability that is explained by the model

Question 17

R^2

Answer 17

The percent of response variable variability that is explained by the model; SSR/SST; would like 100%

Question 18

Linear regression assumptions

Answer 18

LINE + no multicollinearity:
required:
Linearity: relationship between the Xs and the Y variable should be linear in form
response variable is quantitative

interpretable results:
Multicollinearity: no strong multicollinearity between the X variables

best model assumptions:
Independence: true errors are independent
Normality: true errors are normally distributed
Equal variance: variance of Y at each combination of X is equal