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A Function is special relationship where each input has an output
A Function is special relationship where each input has an output.
A function is often written as f(x) where x is the input:
// Generate values var xValues = []; var yValues = []; for (var x = 0; x <= 10; x += 1) { xValues.push(x); yValues.push(x); } // Display using Plotly var data = [{x:xValues, y:yValues, type:"lines"}]; var layout = {title: "f(x) = x"}; Plotly.newPlot("myPlot1", data, layout);
Results from f(x) = x
| x | y | y = x |
|---|---|---|
| 1 | 1 | y = x = 1 |
| 2 | 2 | y = x = 2 |
| 3 | 3 | y = x = 3 |
| 4 | 4 | y = x = 4 |
| 5 | 5 | y = x = 5 |
// Generate values var xValues = []; var yValues = []; for (var x = 0; x <= 10; x += 1) { xValues.push(x); yValues.push(x*2); } // Display using Plotly var data = [{x:xValues, y:yValues, type:"lines"}]; var layout = {title: "f(x) = 2x"}; Plotly.newPlot("myPlot2", data, layout);
Results from f(x) = 2x
| x | y | y = 2x |
|---|---|---|
| 1 | 2 | y = 2x = 2 |
| 2 | 4 | y = 2x = 4 |
| 3 | 6 | y = 2x = 6 |
| 4 | 8 | y = 2x = 8 |
| 5 | 10 | y = 2x = 10 |
A Linear Equation is an equation for a straight line:
var exp1 = "x"; var exp2 = "x*2"; var exp3 = "x*2 + 7"; // Generate values var x1Values = []; var x2Values = []; var x3Values = []; var y1Values = []; var y2Values = []; var y3Values = []; for (var x = 0; x <= 10; x += 1) { x1Values.push(x); x2Values.push(x); x3Values.push(x); y1Values.push(eval(exp3)); y2Values.push(eval(exp2)); y3Values.push(eval(exp1)); } // Define Data var data = [ {x: x1Values, y: y1Values, mode:"lines"}, {x: x2Values, y: y2Values, mode:"lines"}, {x: x3Values, y: y3Values, mode:"lines"} ]; var layout = {title: "[y=" + exp3 + "] [y=" + exp2 + "] [y=" + exp1 + "]"}; // Display using Plotly Plotly.newPlot("myPlot4", data, layout);
A Linear Equation can NOT contain exponents or square roots:
A Linear regression tries to model the relationship between two variables by fitting a linear graph to data.
One variable (x) is considered to be data, and the other (y) is considered to be dependent.
For example, a Linear Regression can be a model to relate the price of houses to their size.
Linear algebra is used to solve Linear Equations.
Linear Least Squares (LLS) is a set of formulations for solving statistical problems involved in Linear Regression.