Unit 2

Question 1

what does the response variable measure?

Answer 1

the outcome of a study
also known as dependent variable

Question 2

what does the explanatory variable attempt to explain?

Answer 2

the observed outcome of the study
also known as independent variable

Question 3

what is an example of the explanatory variable and a response variable?

Answer 3

explanatory variable- mothers height
response variable- daughters height
the variation in daughters height and how its explained in the mothers height

Question 4

where is the explanatory variable and response variable located on a graph?

Answer 4

explanatory variable: x- axis
response variable: y-axis

Question 5

how can we measure the degree of linear association between two quantitative variables?

Answer 5

by determining the correlation

Question 6

what is correlation?

Answer 6

a statistical measurement of the relationship between two quantitative variables

Question 7

what does correlation measure?

Answer 7

the strength and direction of a linear relationship

Question 8

what happens when two variables are positively associated?

Answer 8

as values of X increase, values of Y also tend to increase
the graph will have points that are plotted from the bottom left to the top right

Question 9

what happens when two variables are negatively associated?

Answer 9

as values of X increase, values of Y tend to decrease
the graph will have points that are plotted from the top right to the bottom left

Question 10

what happens when two variables have no association?

Answer 10

points are randomly scattered throughout the scatterplot

Question 11

what is the correlation coefficient?

Answer 11

r

Question 12

what does correlation measure?

Answer 12

the direction and strength of a LINEAR relationship
r ranges from -1 to +1

Question 13

when is direction positive?

Answer 13

is positive when individuals with higher X values tend to have higher values of Y

Question 14

strength

Answer 14

how closely the points follow a straight line

Question 15

weak positive association

Answer 15

0 –> 0.5

Question 16

moderate positive association

Answer 16

0.5 –> 0.8

Question 17

strong positive association

Answer 17

0.8 –> 1

Question 18

weak negative association

Answer 18

-0.5 –> 0

Question 19

moderate negative association

Answer 19

-0.8 –> -0.5

Question 20

strong negative association

Answer 20

-1 –> -0.8
*positive and negative correlation r

Question 21

can the correlation coefficient r be used if a scatterplot shows a curved relationship?

Answer 21

no,
correlation coefficient only describes linear relationships

Question 22

does changing the units in x or y change the value of r?

Answer 22

no

Question 23

does r have units?

Answer 23

no

Question 24

what is x bar (x̄)?

Answer 24

x sample mean

Question 25

what is y bar (ȳ)?

Answer 25

y sample mean

Question 26

what is Sx?

Answer 26

x sample standard deviation

Question 27

what is Sy?

Answer 27

y sample standard deviation

Question 28

what variables does r require?

Answer 28

quantitative variables

Question 29

does it make a difference which variable you denote x and which you denote y to?

Answer 29

no

Question 30

what numbers does r lie between?

Answer 30

-1 and +1 inclusive

Question 31

what does positive r imply?

Answer 31

positive linear association

Question 32

what does negative r imply?

Answer 32

negative linear association

Question 33

what does b0 stand for?

Answer 33

y-intercept

Question 34

what does b1 stand for?

Answer 34

slope (rise/ run)

Question 35

what does the regression line do?

Answer 35

summarizes the relationship between two variables only when one of the variables helps predict or explain the other

Question 36

what does regression describe?

Answer 36

a relationship between an explanatory variable and a response variable

Question 37

what does correlation measure?

Answer 37

the direction and strength of a linear relationship between two quantitative variables

Question 38

do slope and correlation have the same sign? explain

Answer 38

yes, when r= (+), slope will also be (+) because the line is going in an upwards direction when r=(-), slope will also be (-) because the line is going in a downwards direction

Question 39

what is the equation for slope?

Answer 39

Y2 - Y1 / X2- X1

Question 40

what is y hat (ŷ)?

Answer 40

the predicted value of the response variable for x, a certain value of the explanatory variable

Question 41

what is the value of the intercept definition?

Answer 41

the predicted value of the response variable y when x=0, however this prediction MAY NOT BE RELIABLE

Question 42

how is the slope interpreted?

Answer 42

for every one unit increase in the explanatory variable (independent, x) the response variable (dependent, y) is predicted to either increase or decrease by the value of b1 (depending on if b1 is positive or negative)

Question 43

what is the least squares regression line definition?

Answer 43

the line that minimizes the sum of the squares of the residuals

Question 44

what is the residual?

Answer 44

the distance from our observed y value to our line

Question 45

what does the least squares regression line predict?

Answer 45

what y may be predicted to be for various values of x

Question 46

what is extrapolation?

Answer 46

the equation is only correct for the range of values that were included in the study for example, when you fill in an x value in the least squares regression line that isnt apart of/ within the data, the equation is no longer correct

Question 47

what is the equation for residual?

Answer 47

residual = observed y - predicted y residual = yi - ŷi

Question 48

points that fall above our least squares regression line have what sign for a residual?

Answer 48

positive

Question 49

what is r^2?

Answer 49

the coefficient of determination tells us how well our response variable is actually being explained by our explanatory variable

Question 50

what should we automatically think when we see "percentage of variation" or "fraction of variation"?

Answer 50

r^2

Question 51

what is an outlier, in respect to residuals?

Answer 51

an observation with an extremely large residual

Question 52

if there is a point to the extreme left or right of data, what is that called?

Answer 52

influential observation

Question 53

what are points that are outliers in the y direction known as?

Answer 53

outliers

Question 54

what are points that are outliers in the x direction known as?

Answer 54

influential observations

Question 55

what is a lurking variable?

Answer 55

a variable that is not being studied but it may influence the relationship between the two variables being studied

Question 56

regression and correlation are used for what type of association?

Answer 56

linear

Question 57

are regression and correlation affected by extreme outliers?

Answer 57

YES

Question 58

does extrapolation yield reliable predictions?

Answer 58

no (its too risky)

Question 59

what does a strong correlation NOT imply?

Answer 59

a cause and effect relationship

Question 60

do correlation and regression imply causation?

Answer 60

no

Question 61

what is confounding?

Answer 61

when the effects of the explanatory variable on the response is mixed up with the effects of other explanatory variables on the response