Unit 2

Question 1

What is a scatterplot used for

Answer 1

Immediate visual impression of a possible relationship between 2 variables.

Question 2

What is the correlation coefficient

Answer 2

Used as a quantitative value of strength and direction of a linear relationship.

Question 3

Inequality of value of correlation coefficient and symbol

Answer 3

-1 < r < 1

Question 4

What is r^2

Answer 4

Coefficient of determination - % of variation in the resp var that is explained by the explanatory var

Question 5

How is r^2 represented

Answer 5

As a %

Question 6

what does 100% r^2 mean

Answer 6

Perfect fit

all variation in x

Question 7

How to describe a scatter plot and eg

Answer 7

Direction
Form
Strength

Strong positive linear association

Question 8

What are the boundaries of r (what value of r is strong, etc)

Answer 8

r > 0.8 = strong
0.7 < r < 0.8 = moderately strong
r < 0.7 = weak

Question 9

What is a residual

Answer 9

Difference between an observed and predicted value

= actual - predicted

Question 10

Sum and mean of residuals is always equal to

Answer 10

0

Question 11

Line of regression eqn and what each variable is

Answer 11

y hat = a + bx

a = y intercept
b = slope

Question 12

How to calculate B

what does each variable mean

Answer 12

r * sy/sx

r = correlation coeff
sy = SD of y
sx = SD of x

Question 13

How to check if linear model is a good fit

Answer 13

r^2 should be high

Residual plot shouldn’t show any pattern

Question 14

How and whyto transform a graph

Answer 14

Use log or ln on one of the variables, may allow for a linear model to be used

Question 15

How to assess the effectiveness of transformation

Answer 15

Checking if randomness in residual plot has increased

Checking if r^2 value has increased

Question 16

What is the LSRL

Full form

Answer 16

Least squared regression line

Linear model that minimizes the sum of squared

Question 17

If residuals is negative then

if residuals is positive then

Answer 17

Negative - overestimated the response var

Positive - underestimated the response var

Question 18

what is the response var

Answer 18

The dependent var

Question 19

What is the explanatory var

Answer 19

the independent var

Question 20

How to use residual plot to assess good fit (criteria)

Answer 20

Random
Centered at 0
No clear patterns

Question 21

What does a residual plot do

Answer 21

Helps decide if you should use a linear model or should consider others.

Question 22

What is extrapolation

why is it bad

Answer 22

Prediction that was made outside the interval of current data x values.
Trends may not continue at this next X value so it may not be accurate.

Question 23

How to interpret slope

Answer 23

For every ‘x units’ of ‘independent var’, model predict an average increase of ‘slope value’ of ‘dependent var units’

Question 24

How to interpret y intercept

Answer 24

When ‘explanatory var’ = 0, model predicts that the ‘resp value’ woudl be ‘y int value’

Question 25

How to interpret r^2

Answer 25

‘r^2’ percent of var in ‘resp var’ can be explained by the linear relationship with the ‘explanatory var’

Question 26

If r^2 is closer to 0 then

if r^2 is closer to 1 then

Answer 26

r^2 closer to 0 = weak relationship

r^2 closer to 1 = strong relationship.

Question 27

If slope is positive then r is

Answer 27

Positive

Question 28

What is a high leverage point

if removed then what
what does it change

Answer 28

Points with unusually large or small x values far away from xbar (mean of x values)

Cause a substantial shift in the model being used

Slope or y int could be changed.

Question 29

What does an outlier affect

Answer 29

R
R^2
Strength of the model

Question 30

What is an influential point
3 types
what do they affect

Answer 30

Points that when removed change the slope, y int and/or correlation coeff substantially

Outliers (corr)
High lvg pt (change slope/y int)
both of the above