• Making computers that think?
• The automation of activities we associate with human thinking, like decision making, learning … ?
• The art of creating machines that perform functions that require intelligence when performed by people ?
• The study of mental faculties through the use of computational models ?
• Anything in Computing Science that we don't yet know how to do properly ? (!)

• Determine how humans think;
• Get inside the actual workings of human minds;
  • Introspection - catch our own thoughts as they go by;
  • Psychological experiments;
• Sufficiently precise theory of the mind:
  • Express the theory as a computer program;

If the program's input/output and timing behavior matches human behavior, that is evidence that some of the program's mechanisms may also be operating in humans;

• Intelligent behavior as the ability to achieve human-level performance in all cognitive tasks, sufficient to fool an interrogator.

• Uses the "Imitation Game"
• Usual method:
  • Three people play (man, woman, and interrogator)
  • Interrogator determines which of the other two is a woman by asking questions
    • Example: How long is your hair?
  • Typewritten or repeated by an intermediary

• Requires success in:
  • Natural language processing: communicate with the interrogator;
  • Knowledge representation: store and retrieve what it knows;
  • Automated reasoning: use the stored information to answer questions and to draw new conclusions;
  • Machine learning: adapt to new circumstances and to detect and extrapolate patterns

The art of creating machines that perform functions that require intelligence when performed by people. (Kurzweil)

The study of how to make computers do things at which, at the moment, people are better. (Rich and Knight)

The study of mental faculties through the use of computational models. (Charniak and McDermott, 1985)

The study of the computations that make it possible to perceive, reason, and act. (Winston, 1992)

A field of study that seeks to explain and emulate intelligent behavior in terms of computational processes. (Schalkoff, 1990)

The branch of computer science that is concerned with the automation of intelligent behavior. (Luger and Stubblefield, 1993)

• Regression analysis is used to describe the relationship between:
• A single response variable: \(Y\) ; and
• One or more predictor variables: \(X_1\), \(X_2\),…, \(X_n\)
  • n = 1: Simple Regression
  • n > 1: Multivariate Regression

The car R library: Companion to Applied Regression

install.packages("car")

library(car);

Uncompress dataset

data("mtcars")

Load the dataset into a variable

cars.dataset <- mtcars;

Check the first lines of the dataset:

head(cars.dataset);

##                    mpg cyl disp  hp drat    wt  qsec vs am gear carb
## Mazda RX4         21.0   6  160 110 3.90 2.620 16.46  0  1    4    4
## Mazda RX4 Wag     21.0   6  160 110 3.90 2.875 17.02  0  1    4    4
## Datsun 710        22.8   4  108  93 3.85 2.320 18.61  1  1    4    1
## Hornet 4 Drive    21.4   6  258 110 3.08 3.215 19.44  1  0    3    1
## Hornet Sportabout 18.7   8  360 175 3.15 3.440 17.02  0  0    3    2
## Valiant           18.1   6  225 105 2.76 3.460 20.22  1  0    3    1

• Model a continuous variable \(Y\) as a mathematical function of one or more \(X\) variable(s);
• Predict the \(Y\) when \(X\) is known;
• This mathematical equation can be generalized as follows:

\[ \widehat{Y}=\beta_0 + \beta_1X_1 + \beta_2X_2+...+\beta_nX_n \] * The predictors \(X_1\),…, \(X_n\) can be continuous, discrete or categorical variables.

\[ Y=\beta_0 + \beta_1X+\epsilon \]

• \(\beta_0\) (Intercept): point in which the line intercepts the y-axis;
• \(\beta_1\) (Slope): increase in Y per unit change in X.

We want to find the equation of the line that “best” fits the data. It means finding \(b_0\) and \(b_1\) such that the fitted values of \(y_i\), given by \[ \hat{y_i} = b_0+b_1x_i \] are as “close” as possible to the observed values \(y_i\).

Residuals *The difference between the observed value \(y_i\) and the fitted value $:

\[ e_i = y_i − \hat{y_i} \]

A usual way of calculating \(b_0\) and \(b_1\) is based on the minimization of the sum of the squared residuals, or residual sum of squares (RSS): \[\begin{eqnarray} RSS &=& \sum_{i}e_i^2 \\ &=& \sum_{i}(y_i - \hat{y}_i)^2\\ &=& \sum_{i}(y_i - b_0 + b_1x_i) \end{eqnarray}\]

Regression in R with lm() function:

cars.lm1 <- lm(mpg ~ hp, data = cars.dataset);
plot(x=cars.dataset$hp, y=cars.dataset$mpg);
abline(cars.lm1);

\(R^2\):

• Provides an alternative measure to RSE;
• "Unitless";
• The proportion of variance explained;
• Always takes on a value between 0 and 1;
• Independent of the scale of \(Y\);