Unit 3 Flashcards
Linear Regression
What does r tell us?
How STRAIGHT a positive or negative relationship is between TWO QUANTITATIVE variables
What values can r be?
from -1 to 1
Give some strong r values and some weak r values.
Strong r values are close to 1 or -1, like -0.83 or 0.94. Weak r values are close to zero like 0.10 or -0.06
If something is correlated is it associated?
Yes (if it is straight)
association or correlation?
association is talking about a relationship? correlation is an actual calculated number
How to describe association on scatterplot?
DIRECTION… FORM.. STRENGTH (and outliers)
direction?
positive or negative
form?
Linear or nonlinear (straight, curved)
strength?
give the r value (if straight), or say? “tightly packed” or “ loosely packed”
does correlation mean causation?
NO WAY!
Give example of incorrectly using the word “correlation”
“There is a correlation between gender and video game playing.” This person should say “association.” You can’t say correlation because gender is categorical.
Does high r value mean anything?
An r value alone tells little. CHECK THE SCATTERPLOT… IS IT LINEAR?? make sure it’s linear first.
How can you check for “straight enough?”
by looking at the residuals plot
how do you interpret slope?
“For an increase of 1 [unit of x] there is an (increase/decrease) of [SLOPE] [units of y]” Plug in your slope and your units!!!
how do you interpret y intercept?
“The model predicts that if there were no [x stuff] this is how much [y stuff] you’d have” Plug in the appropriate contexts.
how to interpret slope EQUATION? rSy/Sx
For each increase of 1 standard deviation in x direction, you go r *(standard deviation) in y direction.
if you multiply or divide the x’s or y’s (shift/scale) does r change?
No change. r does not have any units so the strength of the line will not change.
If you switch x and y does r change?
No change, the strength will stay the same.
if you switch x and y will slope change?
YES- slope is rsy/sx
Can you predict an X by using a Y?
NOT WITH THE SAME EQUATION! BE CAREFUL!! You have to change the entire equation and start from scratch.
What point does every regression line pass through?
the mean-mean point. (x bar, y bar)
Why is it called “least squares regression line”?
After you find the mean-mean point, you fix the line so that it minimizes the squared vertical distance to that line (minimizes the squared residuals)
interpret r squared
r squared is the % of variability in y that can be explained by the linear model.
does high r squared mean a good model?
CHECK STRAIGHTNESS FIRST. you should check your plot and residuals to make sure model is appropriate and no outliers present? then it means something
is r sensitive to outliers?
yes. A single outlier can make it seem like there is a relationship (out in x direction..), or that there is none.
What is a residual?
ACTUAL minus PREDICTED. A-P
What are b1 and bo ?
b1 is the SLOPE, and bo is the y- intercept.
what is the LSRL
least squares regression line
What should we look for in residual plot?
curve or pattern. Also, it should have equalish scatter from left to right
Which is explanatory variable?
x. horizontal axis. it “explains” what happens to y
which is response?
y.. Vertical axis.. It “responds” to the x
will residual plots always show outliers? (will outliers always have large residuals?)
Not necessarily.. Some points have so much leverage, they pull the line up to it?
How do you get equation from computer output?
y= b0 + b1 x or y=a+bx
y is the dependent variable
b0 is the coefficient of constant (or it says intercept)
b1 is the coefficient of the variable given (independent)
x is the independent variable
What does “y-hat” mean?
The prediction equation for y.
