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What does a subscript do in math?
Subscripts are often used to refer to members of a mathematical sequence or set or elements of a vector. For example, in the sequence O = (45, −2, 800), O3 refers to the third member of sequence O, which is 800.
What is the general regression equation?
A linear regression line has an equation of the form Y = a + bX, where X is the explanatory variable and Y is the dependent variable. The slope of the line is b, and a is the intercept (the value of y when x = 0).
How do you use subscripts in an equation?
In Office’s built-in equation editor you can type ^ (caret) for superscript followed by your text, and subscript is _ (underscore) followed by the text.
What is subscript explain?
A subscript is a character, usually a letter or number, that’s printed slightly below and to the side of another character. Subscripts are commonly used in chemical formulas. A scientist would write the formula for water, H2O, so that the 2 appears lower and smaller than the letters on either side of it.
What does the subscript I mean in multiple linear regression?
The subscript i refers to the i^ { extrm {th}} individual or unit in the population. In the notation for the x- variables, the subscript following i simply denotes which x -variable it is. The word “linear” in “multiple linear regression” refers to the fact that the model is linear in the parameters, \\beta_0, \\beta_1, \\ldots, \\beta_k.
Is there a residual ε in the least squares regression?
There will be a residual ε (epsilon), so that the measured value yj will be This is the least squares regression model . As with the sample, the number subscripts refer to properties of the whole population and the letter subscripts go with particular points.
What is the formula for multiple linear regression?
extrm {MSE}=\\frac { extrm {SSE}} {n- (k+1)} estimates \\sigma^ {2}, the variance of the errors. In the formula, n = sample size, k +1 = number of \\beta coefficients in the model (including the intercept) and extrm {SSE} = sum of squared errors. Notice that simple linear regression has k =1 predictor variable, so k +1 = 2.
What is the formula for MSE in linear regression?
Notice that simple linear regression has k =1 predictor variable, so k +1 = 2. Thus, we get the formula for MSE that we introduced in that context of one predictor. S=\\sqrt {MSE} estimates σ and is known as the regression standard error or the residual standard error.