UNIT 2 VOCAB AND CONCEPTS Flashcards
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
What are 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
What if a scatterplot goes straight across horizontally?
NO ASSOC. That would be like height and IQ. If each height has about the same IQ, then they are INDEPENDENT
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?
straight, curved
strength?
give the r value (if straight), or say? “tightly packed” or “ loosely packed”
does correlation mean causation?
NO WAY DUDE
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 SCATTER.. IS IT LINEAR?? make sure it’s linear first.
How is r calculated?
r= sum(ZxZy) / (n-1)—- the sum of rectangle areas on standardized axes
how can you check for “straight enough?”
residuals plot fool!
how do you interpret slope?
for an increas of 1 [unit of x] there is an (increase/decrease) of [SLOPE] [units of y]
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
how to interpret slope EQUATION? rSy/Sx
for each increase of 1 st dev in x direction, you go r st dev in y direction.
If r= 0.8.. An x value that is 2 standard deviations above the mean will have a predicted y value that is _______
1.6 standard deviations above the mean
if you mult or divide the x’s or y’s (shift/scale) does r change?
no. the strength remains the same. (If you log or square it, it will change, but just adding or multiplying won’t change it)
if you switch x and y does r change?
NO. The strength stays the same.
if you switch x and y will slope change?
YES- slope is rsy/sx? to get new slope you do: (r sqared)/old slope
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 is on every regression line?
the mean-mean point. (x bar, y bar)
Why is it calle d “least squares regression line?”
Because, 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 % of variability in y can be explained by the model. The rest is in residuals?
does high r squared mean a good model?
CHECK STRAIGHNESS 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.
Look for lurking variables?
think hot chocolate sales in caf at wachusett mountain and ski accidents at wachusett mountain. Did the chocolate cause the accident??????
outliers in regression?
doesn’t follow the “flow” (pinky trick)
what about your calculator for using curves to fit curved data?
sure.. Quadreg, cubicreg, lnreg, etc? just be careful when substituting while writing the equation given.
what does “regression to the mean” mean?
preditions for y are closer to the mean y (y bar) than the actual x is to the mean x (in s.d). Sons were closer to average height than the dads. Super tall dads had tall sons, but not super tall sons, on average.
what does influential mean?
It means that the point, when added or removed to data, will influence the SLOPE.. Generally these are outliers in the x direction?. Far left or right.
what is a linear model?
it is an equation you can use? or a line of a graph, but it is just a model that says what kind of happens, and can be used to ESTIMATE WHAT MIGHT HAPPEN
what is a residual?
ACTUAL-PREDICTED. A-P. like this class.. AP (get it?)
what is b1 and bo ?
b1 is the SLOPE, and bo is the intercept. Remember that bo can be thought of as “b old” it is the old b? the intercept in y=mx+b? so it is still the intercept.
what is leverage?
leverage just means it is far away from x-bar? far right or left from the middle.. Some leverage points are not influential if they go along with the flow of the scatter.
what is the line that you plot?
IT IS A MODEL!
what is the LSRL
the “least squares regression line” that line.. That equation
what should we look for in resid plot?
curve or pattern.. Also, it should have equalish scatter from left to right
what’s up with extrapolation?
not a good idea. sometimes it’s all you can do, but still, NOT GOOD
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?
What is homoscedasticity?
equal scatter along the regression line
What if the scatterplot is curved?
either straighten it and fit a line, or keep it and fit a curve (quadreg, cubicreg, lnreg, logreg)
How can you straighten data?
Do stuff to the y (square it, root it, log it, etc) and recheck the plot. Remember to put the transformation into your equation.. Example Sqrt y = 4.33 - 2.03 x
How do you undo a log when solving?
10^ stuff
How do you undo an ln when solving?
e^stuff
How do you undo sqrt when solving?
^2
How do you undo squares or cubes?
^ 1/2 or ^ 1/3
How do you get equation from computer output?
y= b0 + b1 x
y is the dependent variable
b0 is the coefficient of constant (or it says intercept)
b1 is the coefficient of the variable given (indep)
x is the indep variable
generally arranged: Y= this down plus this left “
