UNIT 2 - REGRESSION

Question 1

How do you describe a scatterplot?

Answer 1

DIRECTION

Unusual Features

FORM

STRENGTH

Question 2

describe a scatterplot’s strength?

Answer 2

give the r value (if straight),

or say…

“tightly packed… loosely packed”

Question 3

how do you describe direction?

Answer 3

positive or negative

Question 4

how do you describe form of a scatterplot?

Answer 4

straight or curved?

Question 5

Diff between association or correlation?

Answer 5

association is talking about a relationship.

If you see a pattern in the scatterplot, there is an association.

Correlation is an actual calculated number (two quantitative variables)

Question 6

Why is it called the “least squares regression line?”

the LSRL?

Answer 6

Because, after you find the mean-mean point, you fix the line so that it minimizes the squared vertical distancesto that line from each point.

It minimizes the squared residuals, the least squares….

Question 7

How do you find outliers in regression?

Answer 7

they don’t follow the “flow”

(pinky trick, cover with you pinky.. Then uncover.. Does it follow the flow?)

Question 8

What values can r be?

Answer 8

from -1 to +1

(r near 0 is WEAK)

Question 9

What is the line that you plot?

Answer 9

IT IS A MODEL!

It is the LSRL and it is the model we are talking about

Question 10

what is a linear model?

Answer 10

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

Question 11

What does r² tell us?

(r-squared)

Answer 11

It tells us the percent of variablility of y that is explained by the model with x.

Question 12

What if a scatterplot goes straight across horizontally?

Answer 12

NO ASSOCIATION.

That would be like height and IQ, they are independent so each height has about the same IQ.

Question 13

Does r² tell direction?

Answer 13

NO

r² is always positive, so you can’t use it to see if the relationship is negative.

Question 14

Can there be a correlation between grade and music preference?

Answer 14

No, music preference is categorical.

There is an association, however.

Question 15

Does the regression line (LSRL) go through a lot of points?

Answer 15

No, usually it goes through NONE!

It just goes through the center of the cloud of points.

Question 16

Does a high r value mean anything?

(can it look strong, but not be?)

Answer 16

Sure. It can. It tells you strength of LINEAR relationship.

BUT

CHECK THE SCATTER. One outlier can make it look STRONG.

Question 17

what is the LSRL

Answer 17

the “least squares regression line”

that line you plot

OR

That equation

Question 18

What does r tell us?

Answer 18

The direction (+/-) and how strong a LINEAR relationship is between two QUANTITATIVE variables… (when linear)

Question 19

which is response?

Answer 19

y variable,

the Vertical axis..

It “responds” to the x

Question 20

what is b₁ and b_o ?

Answer 20

b₁ is the SLOPE,

b_o is the intercept.

Question 21

What’s wrong: Age and height have a correlation of 2.7

Answer 21

WRONG.

Correlation must be between 1 and -1

Question 22

What should we look for in resid plot?

Answer 22

Curve or pattern.

Also, it should have equalish scatter from left to right

It should look RANDOM

Question 23

What if the scatterplot is curved?

Answer 23

Straighten the scatter and fit a line,

check the graph and the r.

Question 24

What is extrapolation?

Answer 24

Making predictions outside of the x values you have.

Question 25

does correlation mean causation?

Answer 25

NO WAY DUDE

Question 26

What’s up with extrapolation? Is it OK?

Answer 26

Not ideal. Sometimes it’s all you can do, but state CAUTION.

Question 27

will residual plots always show outliers?

(will outliers always have large residuals?)

Answer 27

Not necessarily. Some points have so much leverage, they pull the line up to it…

Question 28

How can you check for “straight enough?”

Answer 28

Residuals plot fool!

check the resids

Question 29

What are some strong r values and some weak r values

Answer 29

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

Question 30

What point is on every regression line?

Answer 30

the mean-mean point. (x bar, y bar).

This point is generally not one of the points on the scatterplot.

Usually none of the scatterplot points are on the regression line.

Question 31

Which is explanatory variable?

Answer 31

the x

the horizontal axis.

it “explains” what happens to y

Question 32

What do we look for in a residuals plot?

Answer 32

To proceed, it should look random.

if there is a pattern, then find a new model or proceed with caution.

Question 33

What is a residual?

Answer 33

Vertical distance to the LSRL.

ACTUAL-PREDICTED,

A-P, like this class AP (get it?)

Take y data found and from that, subtract the y you get from plugging the x into the model (equation).

Question 34

is r sensitive to outliers?

Answer 34

yes. A single outlier can make it seem like there is a relationship ( if way out in x direction), or even seem like there is no relationship.

Question 35

what is leverage?

Answer 35

Far right or left from the middle.

leverage just means it is far away from x-bar

Some leverage points are not influential if they go along with the flow of the scatter.

Question 36

Interpret residual: Points below the line/negative resid

Answer 36

“the model overpredicted”

or

“Actual value was below the the expected (or predicted)”

Question 37

Interpret residual: Points above the line/positive resid

Answer 37

“the model underpredicted” or “actual performance was above the expected performance

Question 38

Does high r squared mean a good model?

Answer 38

CHECK SCATTER FIRST..

Make sure model “FITS” the data.

You should check your scatterplot and residuals plot to make sure model is appropriate and no outliers present… then it means something

So YES, but after you check the resids.

Question 39

How do you interpret slope?

Answer 39

For an increase of 1 [unit of x] there is an (increase/decrease) of [SLOPE] [units of y].

You can write “SLOPE UNITS Y/ ONE UNITS X” to help

Question 40

what does influential mean?

Answer 40

It impacts the SLOPE.

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.

Question 41

if you switch x and y does r change?

Answer 41

NO. The strength stays the same.

Question 42

Interpret r squared

Answer 42

r squared % of variability in y can be explained by the model with x. The rest is in residuals…

Question 43

If there is a crazy outlier, what can you do?

Answer 43

Run the analysis with and without the outlier and write about both.

Question 44

how do you interpret y intercept?

Answer 44

The model predicts that if there were no [x stuff] this is how much [y stuff] you’d have

Question 45

How do you get equation from computer output?

variable coeff indep: age

constant 7.2

Height 3.5

Answer 45

For this case:

age = 7.2 + 3.5 (height)

Question 46

Computer ouput:

What does “constant” mean?

Answer 46

It is the y intercept

Question 47

Computer Output:

What is “S”

Answer 47

The average, or typical residual..

Standard deviation of the residuals

typical distance from actual value to the model’s prediction.

About how far off your prediction is likely to be.

Question 48

How can you straighten data?

Answer 48

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