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Stat 1000 > Unit 2 > Flashcards

Unit 2 Flashcards

1
Q

what does the response variable measure?

A

the outcome of a study
also known as dependent variable

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2
Q

what does the explanatory variable attempt to explain?

A

the observed outcome of the study
also known as independent variable

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3
Q

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

A

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

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4
Q

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

A

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

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5
Q

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

A

by determining the correlation

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6
Q

what is correlation?

A

a statistical measurement of the relationship between two quantitative variables

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7
Q

what does correlation measure?

A

the strength and direction of a linear relationship

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8
Q

what happens when two variables are positively associated?

A

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

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9
Q

what happens when two variables are negatively associated?

A

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

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10
Q

what happens when two variables have no association?

A

points are randomly scattered throughout the scatterplot

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11
Q

what is the correlation coefficient?

A

r

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12
Q

what does correlation measure?

A

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

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13
Q

when is direction positive?

A

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

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14
Q

strength

A

how closely the points follow a straight line

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15
Q

weak positive association

A

0 –> 0.5

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16
Q

moderate positive association

A

0.5 –> 0.8

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17
Q

strong positive association

A

0.8 –> 1

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18
Q

weak negative association

A

-0.5 –> 0

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19
Q

moderate negative association

A

-0.8 –> -0.5

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20
Q

strong negative association

A

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

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21
Q

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

A

no,
correlation coefficient only describes linear relationships

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22
Q

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

A

no

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23
Q

does r have units?

A

no

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24
Q

what is x bar (x̄)?

A

x sample mean

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25
Q

what is y bar (ȳ)?

A

y sample mean

26
Q

what is Sx?

A

x sample standard deviation

27
Q

what is Sy?

A

y sample standard deviation

28
Q

what variables does r require?

A

quantitative variables

29
Q

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

A

no

30
Q

what numbers does r lie between?

A

-1 and +1 inclusive

31
Q

what does positive r imply?

A

positive linear association

32
Q

what does negative r imply?

A

negative linear association

33
Q

what does b0 stand for?

A

y-intercept

34
Q

what does b1 stand for?

A

slope (rise/ run)

35
Q

what does the regression line do?

A

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

36
Q

what does regression describe?

A

a relationship between an explanatory variable and a response variable

37
Q

what does correlation measure?

A

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

38
Q

do slope and correlation have the same sign? explain

A

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

39
Q

what is the equation for slope?

A

Y2 - Y1 / X2- X1

40
Q

what is y hat (ŷ)?

A

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

41
Q

what is the value of the intercept definition?

A

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

42
Q

how is the slope interpreted?

A

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)

43
Q

what is the least squares regression line definition?

A

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

44
Q

what is the residual?

A

the distance from our observed y value to our line

45
Q

what does the least squares regression line predict?

A

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

46
Q

what is extrapolation?

A

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

47
Q

what is the equation for residual?

A

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

48
Q

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

A

positive

49
Q

what is r^2?

A

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

50
Q

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

A

r^2

51
Q

what is an outlier, in respect to residuals?

A

an observation with an extremely large residual

52
Q

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

A

influential observation

53
Q

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

A

outliers

54
Q

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

A

influential observations

55
Q

what is a lurking variable?

A

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

56
Q

regression and correlation are used for what type of association?

A

linear

57
Q

are regression and correlation affected by extreme outliers?

A

YES

58
Q

does extrapolation yield reliable predictions?

A

no (its too risky)

59
Q

what does a strong correlation NOT imply?

A

a cause and effect relationship

60
Q

do correlation and regression imply causation?

A

no

61
Q

what is confounding?

A

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

Stat 1000 (5 decks)

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