Exam 2 Flashcards
What is the main assumption of a sample linear regression model?
The relationship between dependent and independent variables is linear.
In simple linear regression, what does the slope of the regression line represent?
The change in the dependent variable for a one-unit change in the independent variable.
What is the objective of the least squares method in simple linear regression?
To minimize the sum of squared differences between observed and predicted values. (residuals)
In the equation Y = B0 + B1X + eY, what does the e/epsilon represent?
The residual or error term.
In multiple linear regression, what is a key difference compared to simple linear regression?
There is more than one independent variable.
What is multicollinearity in multiple linear regression?
When independent variables are highly correlated with each other
How can you reduce multicollinearity in multiple linear regression?
Remove or combine highly correlated independent variables.
In multiple linear regression, what does the adjusted R-squared value represent?
The percentage of total variation explained by the model, adjusted for the number of predictors
When performing multiple linear regression, why is it important to check residual plots?
To check for homoscedasticity and ensure residuals are randomly distributed
In the context of industrial distribution, if we want to predict distribution costs based on distance, product weight, and delivery method, what type of regression would be appropriate?
Multiple Linear Regression
What type of dependent variable is logistic regression used for?
Categorical Variables
In binary logistic regression, what does the odds ratio represent?
The change in odds of the dependent variable being 1 for a one-unit increase in independent variable
In logistic regression, which function is used to transform the linear combination of inputs into a probability?
Sigmoid Function
Which of the following is NOT an assumption of logistic regression?
The residuals must be normally distributed.
What is the role of the activation function in a neuron of an artificial neural network?
To introduce non-linearity into the model and determine if the neuron should be activated.
In a feed-forward neural network, information flows in which direction?
Forward from the input layer to the output layer
In the backpropagation process in an artificial neural network, which of the following is true?
The weights are adjusted to minimize the loss function by calculating gradients
Which of the following is NOT a common activation function used in artificial neural networks?
Softmax
What is logistic regression used for?
Binary values
What are Residuals?
the observed errors associated with estimating the value of the dependent variable using the regression line.
Residual Equation
Actual Y value - Predicted Y value
Standard Residual Equation
residual / standard deviation
What are the four assumptions of linear regressions?
- Linearity
- Normality of Errors
- Homoscedasticity
- Independence of Errors
Explanatory Variables are the same as…
Independent variables and x-variables
Response Variables are the same as…
Dependent variables, Y-variables, & outcome variables
What do you look at to determine if a variable is statistically insignificant?
Look at p-values greater than alpha
What is overfitting?
Fitting a model too closely to the sample data at the risk of not fitting it well to the population in which we are interested
Equation of a Logit model in terms of probability (p)
p = 1 / 1+e^-(regression equation)
The Odds of an event are defined as…
Odds = p / (1-p)
Given the odds of an event, the probability of is defined as…
odds / (1+odds)
What are the three equivalent logit equations?
logit = ln(odds) = ln(p/(1-p)) = B0+B1X
What is Binary Logistic Regression?
The categorical response has only two possible outcomes. Example: Spam or Not
What is Multinomial Logistic Regression
Three or more categories without ordering. example: predicting which food is preferred more (Veg, Non-Veg, Vegan)
What is Ordinal Logistic Regression?
Three or more categories with ordering. Example: move rating from 1 to 5
What are the 7 application areas of ANN?
- Science and Medicine
- Manufacturing
- Marketing and Sales
- Finance
- Banking and Insurance
- Security
- Engineering
What is Machine Learning (ML)?
Type of algorithm that automatically improves itself based on experience, not by a programmer writing a better algorithm.
What are the three types of machine learning?
- Reinforcement Learning
- Unsupervised Machine Learning
- Supervised Machine Learning
An increasingly popular approach to supervised machine learning is…
the neural network
What is an Artificial Neural Network (ANN)?
computational model that is inspired by the way biological neural networks in the human brain process information
What is the goal of the training phase for an ANN?
to determine weights for connections that will correctly classify the training data
the weight control the ____ __ _______
strength of influence
We model the firing rate of the neuron with…
an activation function f
Behavior of an artificial neural network to any particular input depends upon: (3)
- structure of each node (activation function)
- structure of the network (architecture)
- weights on each of the connections
Is an activation function linear or non-linear?
Non-linear
Why are activation functions important?
most real-world data is nonlinear and we want neurons to learn these nonlinear representations
Sigmoid Activation Function
Takes a real-valued input and squashes it to a range between 0 and 1
1 / (1+exp(-x))
Tanh Activation Function
Takes a real-valued input and squashes it to the range [-1,1]
2o(2x)-1
ReLU Activation Function
Stands for Rectified Linear Unit. It takes a real-valued input and thresholds it at zero (replaces negative values with zero)
f(x) = max(0, x)
What is the main function of Bias?
to provide every node with a trainable constant value
A bias allows you to shift the _______ _______ to the left or right.
activation function
Bias helps in ____ ___ ____ at which activation function will trigger
controlling the value
A negative bias shifts the graph which way?
to the right
Feedforward Neural Networks learn though….
backpropagation
Input Nodes
No computation is performed in any of the input nodes
Hidden Nodes
While a feedforward network will only have a single input layer and a single output layer, it can have zero or multiple hidden layers.
Output Nodes
Responsible for computations and transferring information
What is Backpropagation?
The process in which a multilayer perceptron learns
