Multivariable: Linear Regression Flashcards
What is a regression line
a straight line that
describes how a response variable y changes
as an explanatory variable x changes.
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
What is a or b0
a or b0 is a constant
What is b or b1
b or b1 is the slope of the line
What is the least-squares regression
the technique we use to find the line that
best fits the observations.
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)
in multivariable models we have to use the
adjusted R2 bc…
…it includes an adjustment for the
increased number of independent variables.
What is the multivariable equation
y = b0 +b1x1 + b2 x2 + b3x3 +…+ bn xn
How do we predict values of Y
we enter in a vector of covariates
and solve
bo is the value of y when…
x’s = 0 which usually has little meaning
b1…bn are….
interpreted as the amount by which y
changes for each 1 unit change in x HOLDING ALL
OTHER VARIABLES CONSTANT
For ANOVA f test what is the simple linear regression equation
H0: β1= 0 Ha: β1≠ 0
For ANOVA f test what is the multivariate equation
H0: β1,β2,β3,β4= 0 Ha: β1 or β2 or β3 or β4≠ 0
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
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
What is the adjusted r2 value
– the percent of the variation in the outcome that is
explained by the model
What is an F test
the global test of significance of the model; are any of the
independent variables related to the outcome?
yi-y
What is the total variation in the response y is expressed by the deviations
Memorize this
SSR = (measure of explained variation) - REGRESSION SSE = (measure of unexplained variation) - RESIDUAL SST = SSR + SSE = (measure of total variation in y) - TOTAL
