Multivariable: Linear Regression Flashcards Preview

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Flashcards in Multivariable: Linear Regression Deck (19)
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1

What is a regression line

a straight line that
describes how a response variable y changes
as an explanatory variable x changes.

2

what is the formula for a straight line

A straight line relating y to x has an equation of the form:
– y = a + bx
• In this equation, b is the slope
– the amount by which y
changes when x increases by
one unit. The number a is the
intercept, the value of y when x
= 0.
--y = b0 + b1x

3

What is a or b0

a or b0 is a constant

4

What is b or b1

b or b1 is the slope of the line

5

What is the least-squares regression

the technique we use to find the line that
best fits the observations.

6

What is the The Sum of Squares Regression (SSR) and how do you calculate it

The Sum of Squares Regression (SSR) is the sum of the squared differences between the prediction for each observation and the population mean.
SSR + SSE. ((measure of explained variation)+(measure of unexplained variation)

7

in multivariable models we have to use the
adjusted R2 bc...

...it includes an adjustment for the
increased number of independent variables.

8

What is the multivariable equation

y = b0 +b1x1 + b2 x2 + b3x3 +...+ bn xn

9

How do we predict values of Y

we enter in a vector of covariates
and solve

10

bo is the value of y when...

x’s = 0 which usually has little meaning

11

b1...bn are....

interpreted as the amount by which y
changes for each 1 unit change in x HOLDING ALL
OTHER VARIABLES CONSTANT

12

For ANOVA f test what is the simple linear regression equation

H0: β1= 0 Ha: β1≠ 0

13

For ANOVA f test what is the multivariate equation

H0: β1,β2,β3,β4= 0 Ha: β1 or β2 or β3 or β4≠ 0

14

In multivariable models if the p-value ≤ 0.05 then we...

– reject the null hypothesis and conclude that at least one parameter estimate has a significant linear relationship with our outcome

15

In multivariable models if the p-value > 0.05 then we...

fail to reject the null hypothesis and conclude that none of our parameter estimates has a significant linear relationship with our outcome

16

What is the adjusted r2 value

– the percent of the variation in the outcome that is
explained by the model

17

What is an F test

the global test of significance of the model; are any of the
independent variables related to the outcome?

18

yi-y

What is the total variation in the response y is expressed by the deviations

19

Memorize this

SSR = (measure of explained variation) - REGRESSION
SSE = (measure of unexplained variation) - RESIDUAL
SST = SSR + SSE = (measure of total variation in y) - TOTAL