Reading Quiz 3

Question 1

explanatory variable

Answer 1

independent
x
can still use if explanatory doesn’t cause response

Question 2

response variable

Answer 2

dependent

y

Question 3

scatterplots analyzed according to

Answer 3

direction
form
strength of relationship
outliers

Question 4

direction

Answer 4

positive association, negative association, neither

Question 5

form

Answer 5

clusters of points, linear pattern, etc

need to say if linear or not

Question 6

strength of the relationship

Answer 6

how close to a straight line do the points appear to be

Question 7

outliers

Answer 7

points that don’t follow the general pattern of the data

Question 8

correlation coefficient

Answer 8

measures direction and strength of linear relationship between two quantitative variables
r

Question 9

notes about correlation coefficient number

Answer 9

always -1

Question 10

what does correlation coefficient measure

Answer 10

existence and strength of linear relationships

if r=0 not a linear relationship but other relationship could exist

Question 11

is formula for correlation coefficient sensitive to outliers

Answer 11

extremely sensitive

Question 12

does correlation coefficient have units

Answer 12

no

Question 13

does correlation coefficient changed based on explanatory and response variable

Answer 13

no

it is the same regardless of which variable you consider to be the explanatory and which you consider to be the response

Question 14

extrapolation

Answer 14

use of a regression line for predication outside the range of values of the explanatory variable x used to obtain the line
often not accurate
bad

Question 15

least squares regression line

Answer 15

line that makes the sum of the squares of the residuals as small as possible

Question 16

sum of the squares of the residuals

Answer 16

error sum of the squares

Question 17

formula for least squares regression line

Answer 17

yhat = a + bx
b = slope = r(sy/sx)
a = y-intercept = mean of y — mean of x (slope)

Question 18

what point is on every regression line

Answer 18

(mean of x, mean of y)

Question 19

residual

Answer 19

y — yhat
observed value of y minus predicted value of y
positive = above regression line
negative = below regression line

Question 20

coefficient of determination

Answer 20

r^2
measures variation in y that is explained by y’s linear association with x
higher means better LSRL fits

Question 21

sentence for coefficient of determination

Answer 21

this means that X% of the variation in Y (y) is explained by the linear relationship with X (x)

Question 22

residual plot

Answer 22

graphs the residuals on the vertical axis and either explanatory, response, or predicted response values on the horizontal axis

Question 23

residuals from a LSRL always have a mean of

Answer 23

0

Question 24

how data fits residual plots

Answer 24

good if points scattered evenly and closely to horizontal axis, no clear pattern
bad if plot is curved (not linear)
bad if values fan out (outliers, not as accurate on fanned side)

Question 25

outlier

Answer 25

observation that lies outside the overall pattern of the other observations in a scatterplot
can be outlier in x, y, or both directions

Question 26

influential

Answer 26

observation is influential if removing it would markedly change the position of the regression line
points that are outliers in the x direction are often influential

Question 27

are correlation coefficient (r) and LSRL resistant

Answer 27

no

Question 28

scatterplot

Answer 28

displays relationship between two quantitative variables for the same individual

Question 29

least squares regression line

Answer 29

line of best fit
only used when one variable helps explain or predict the other
can be used to predict a y value given an x
minimizes residual

Question 30

clusters

Answer 30

when describing a scatterplot and the values fall in two or more groups separated by gaps

Question 31

for any given x value the more widely varying the y values are means the relationship is

Answer 31

less strong

Question 32

three other scatterplot guidelines

Answer 32

1. make the intervals uniform
2. label both axes
3. choose a scale that makes graph big enough

Question 33

how to add categorical variable into graph

Answer 33

use different colors or symbols

Question 34

which measures of center and spread do you use with the correlation coefficient

Answer 34

mean and standard deviation

Question 35

true or false: in a regression line you get the same numbers (slopes and intercepts) no matter which variable is considered explanatory and which is considered response

Answer 35

false

change per unit of x v y different than change per unit of y v x

Question 36

for LSRL sum of what squares being minimized?

Answer 36

squares of errors for each data point (residuals)

Question 37

SSE

Answer 37

sum of the squares of the deviations of the actual y values from the predicted y values (residuals)

Question 38

true or false: the slope of the regression line tells how many unstandardized units the predicted value of y changes for each unstandardized unit change in x

Answer 38

true

Question 39

true or false: the correlation coefficient tells how many standard deviations the predicted y changes for each standard deviation change in x

Answer 39

true

Question 40

true or false: if both of two variables x and y are standardized so the the sd of both is 1 then the slope of the regression line and the correlation coefficient are equal

Answer 40

true

Question 41

true or false: LSRL is line that minimizes square of residuals

Answer 41

true

Question 42

why can’t all values on residual plot be positive

Answer 42

mean of least squares residuals is zero so if have positive must have negative too

Question 43

does influential point necessarily have large residual

Answer 43

no