Multivariable: Linear Regression

Question 1

What is a regression line

Answer 1

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

Question 2

what is the formula for a straight line

Answer 2

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

Question 3

What is a or b0

Answer 3

a or b0 is a constant

Question 4

What is b or b1

Answer 4

b or b1 is the slope of the line

Question 5

What is the least-squares regression

Answer 5

the technique we use to find the line that

best fits the observations.

Question 6

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

Answer 6

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)

Question 7

in multivariable models we have to use the

adjusted R2 bc…

Answer 7

…it includes an adjustment for the

increased number of independent variables.

Question 8

What is the multivariable equation

Answer 8

y = b0 +b1x1 + b2 x2 + b3x3 +…+ bn xn

Question 9

How do we predict values of Y

Answer 9

we enter in a vector of covariates

and solve

Question 10

bo is the value of y when…

Answer 10

x’s = 0 which usually has little meaning

Question 11

b1…bn are….

Answer 11

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

Question 12

For ANOVA f test what is the simple linear regression equation

Answer 12

H0: β1= 0 Ha: β1≠ 0

Question 13

For ANOVA f test what is the multivariate equation

Answer 13

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

Question 14

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

Answer 14

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

Question 15

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

Answer 15

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

Question 16

What is the adjusted r2 value

Answer 16

– the percent of the variation in the outcome that is

explained by the model

Question 17

What is an F test

Answer 17

the global test of significance of the model; are any of the

independent variables related to the outcome?

Question 18

yi-y

Answer 18

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

Question 19

Memorize this

Answer 19

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