For unlimited access to Class Notes, a Class+ subscription is required.

Tuesday January 11, 2011

Regression equation: y = a + bx

y = the predicted value, or the dependent variable

and x = the independent variable

a = intercept (y when x = 0 )

b = the slope of a line

we're going to discuss this more next week

regression and correlation fit together in a way, since correlation is defined by a regression

equation

people think interval data is more powerful than nominal or ordinal....

bivariate analysis:

if we want to predict y from x the scores from x must be at least as efficient as the scores of y

as the mean of y itself.

So we have two axes and the idea is that there's one independent and one dependent

variable. These variables have ranks that some things are higher than others, and that

there's a constant interval between each of the units. It's measured in some set of units i.e. x

= years of education. Now the idea here is that we can have a number of individual cases

that are ranked on x or ranked on y. the best predictor of y (just y, alone) would be whatever

the mean score of y is. and the reason that it' s the best predictor is that y would give us the

smallest average deviation of the mean of y. so the mean of the sample becomes the standard

of which we compare any other variable.

so the square deviation of the mean score will let us decide if x is useful.

pg. 309 in brians (only just touched upon on that page).

there's more than one kind of variance or variation. in fact there's 3 we need to worry about...

Types of Variation

1) Total Variance

- It equals the sum of the square differences from the mean on any variable

- The average squared deviation = the total variation of the y variable

- "The least squares line"

2) Unexplained Variance

- Everything that's left over (that doesn't touch the regression "slope" aka the

equation

"y = a + bx")

3) Explained Variance

- Total variation of y that can be attributed to the influence of x

- Pearson's correlation = the square root of the variance.

- So r = the square root of explained variance.

www.notesolution.com