http://en.wikipedia.org/wiki/Errors_and_residuals_in_statistics
An "error" is the difference between a measurement and the value it would have had if the process of measurement were infallible and infinitely accurate. If one uses a single observed value as an estimate of the average of the population of values from which it was taken, then that observed value minus the population average is the error.
Sometimes (often) errors are modeled as being distributed normally, with probability distribution
$$
\varphi_\sigma(x)\,dx = \frac 1 {\sqrt{2\pi}} \exp\left( \frac{-1} 2 \left(\frac x \sigma\right)^2 \right) \, \frac{dx} \sigma
$$
with expected value $0$ and standard deviation $\sigma$.
The cumulative probability distribution function is
$$
\Phi_\sigma(x) = \int_{-\infty}^x \varphi_\sigma(x)\,dx.
$$
Up to a rescaling of $x$, this is the error function. The usual definition of the "error function" omits the factor of $1/2$, and thus the standard deviation of the distribution whose cumulative distribution function is the "error function" is not $1$. I am far from convinced that it ought to be rescaled in that way.
Strictly speaking, a probability distribution is a function (more precisely, a measure) that assigns to each event some real number in $[0,1]$. Whenever $X$ is a random variable, giving its probability distribution is giving the probabilities attached to the values that $X$ can take. For example if $X$ is the number given when you roll a die, and if $P_X$ is its probability distribution, then you have $P_X(\{1,2\})={1 \over 3}$, $P_X(\{3\})={1 \over 6}$ and so on. For each event, you assign a real number that is the probability of this event. This function is called the probability distribution of $X$.
Now probability distribution is also used is a broader sense, which is closer to the meaning of statistical model. For example, we say $X$ has the binomial distribution. When we say that, what we really mean is $X$ has a binomial distribution, that is: there exists some $n$ and $p$ such that $X\sim Bin(n,p)$. But strictly speaking, if $X\sim Bin(3,0.2)$ and $Y\sim Bin(3,0.4)$, $X$ and $Y$ don't have the same distribution because the probabilities are not the same. However we talk about the binomial distribution.
That is where the concept of statistical model arises. A statistical model is just a set of probability distributions $\mathcal{P}=\{P_{\theta},\theta\in\Theta\}$. For example $\Theta=(0,1)$ and $P_\theta$ is the $Bin(10,\theta)$ distribution. This is a binomial model. This is used in statistics, when you have observations, but you don't know the underlying probability distribution. Thus we make the hypothesis that it belongs to some set of distributions, which is your model, indexed by a parameter $\theta$. Then, we ask ourselves: based on the observations, what can we say about $\theta$, what is the real underlying distribution? Note that we may be wrong. Maybe the real distribution does not belong to this statistical model.
Short Answer
- A probability distribution is a function that assigns to each event a number in $[0,1]$ which is the probability that this event occurs.
- A statistical model is a set of probability distributions. We assume that the observations are generated from one of these distributions.
Best Answer
What you have made is a linear model. You have made a linear regression that you are using predict future outcomes.
Further information is on this Wikipedia page, specifically:
There are a number of links at the bottom of that page.
I hope this helps