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Biostatistics > Correlation and Regression > Flashcards

Correlation and Regression Flashcards

1
Q

relationship between variables

A

correlation

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2
Q

r = 0 to +1

A

positive correlation

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3
Q

r = 0 to -1

A

negative correlation

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4
Q

height = 50.75 + 0.9741 (femur)

what is the b

A

50.75

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5
Q

height = 50.75 + 0.9741 (femur)

what is the a

A

0.971

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6
Q

height = 50.75 + 0.9741 (femur)

what is the x

A

femur

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7
Q

height = 50.75 + 0.9741 (femur)

what is the y

A

height

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8
Q

height = 50.75 + 0.9741 (femur)

what does the slope tells us

A

the model predicts that each additional increase of femur length, is associated with 0.9741 increase of height

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9
Q

height = 50.75 + 0.9741 (femur)

what is the y intercept

A

50.75

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10
Q

height = 50.75 + 0.9741 (femur)

what does 50.75 mean

A

if there is 0 femur length, 50.75 will be the height

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11
Q

A measure of association between two numerical variables.

A

correlation

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12
Q

Typically, in the summer as the temperature increases people are thirstier.

what type of correlation

A

positive

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13
Q

measures the direction and the strength of the linear association between two numerical paired variables.

A

pearson’s sample correlation coefficient r

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14
Q

as the x variable increases so does the y variable

A

positive correlation

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15
Q

as the x variable increases, the y variable decreases.

A

negative correlation

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16
Q

As the price of an item increases, the number of items sold decreases.

what kind of correlation

A

negative

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17
Q

r value interpretation

1

A

perfect positive linear relationship

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18
Q

r value interpretation

0

A

no linear relationship

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19
Q

r value interpretation

-1

A

perfect negative linear relationship

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20
Q

The strength of the linear association is measured by the

A

sample correlation coefficient r

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21
Q

r value of

0.9

A

strong association

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22
Q

r value of

0.5

A

moderate association

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23
Q

r value of

0.25 weak association

A

weak association

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24
Q

Specific statistical methods for finding the “line of best fit” for one response (dependent) numerical variable based on one or more explanatory (independent) variables.

A

regression

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25
Q

Includes using statistical methods to assess the “goodness of fit” of the model. (ex. Correlation Coefficient)

A

regression

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26
Q

3 main purposes of regression

A

to describe
to predict
to control

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27
Q

model a set of data with one dependent variable and one (or more) independent variables

what purpose of regression

A

to describe

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28
Q

or estimate the values of the dependent variable based on given value(s) of the independent variable(s).

what function of regression

A

to predict

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29
Q

administer standards from a useable statistical relationship

what purpose of regression

A

to control

30
Q

Statistical method for finding
the “line of best fit”

for one response (dependent) numerical variable

based on one explanatory (independent) variable.

A

simple linear regression

31
Q

what is b

y = a + bx

A

slope

32
Q

what is a

y = a + bx

A

y intercept

33
Q

what is r

y = a + bx

A

correlation coefficient

34
Q

what is r^2

y = a + bx

A

coefficient of determination

35
Q

y=1.5*x - 96.9

1.5 oz of water drank
1 degree F increase in temp

what is the slope

A

for each 1 degree F increase in temperature, you expect an increase of 1.5 ounces of water drank.

36
Q

y=1.5*x - 96.9

1.5 oz of water drank
1 degree F increase in temp

what is the y-intercept

A

when the temp is 0 degrees F, then the person would drink about -97 oz of water

37
Q

y=1.5*x - 96.9

1.5 oz of water drank
1 degree F increase in temp

predict the amount of water when the temp is 95

A

45.6 oz

38
Q

tells the percent of the variation in the response variable that is explained (determined) by the model and the explanatory variable.

A

coefficient of determination

39
Q

coefficient of determination tells us

A

the percent of the variation in the response variable that is explained (determined) by the model and the explanatory variable.

40
Q

r2 =92.7%.

what does it mean?

A

About 93% of the variability in the amount of water consumed is explained by the outside temperature using this model

Therefore, 7% of the variation in the amount of water consumed is not explained by this model using temperature

41
Q

application of regression

A

predicting solar maximum
estimating seasonal sales
Predicting Student Grades Based on Time Spent Studying

42
Q

for a regression /correlation problem, first thing to do is to:

A

check for normality

43
Q

descriptives (Shapiro Wilk)

Amount of rainfall in area - 0.968
Quality of air pollution removed - 0.607

which data is normal

A

both is normal

44
Q

hypothesis for the Amount of rainfall (x) and quantity of air pollution removed (y)

A

Ho: there is no significant relationship between the amount of rainfall in an area and the quantity of air pollution removed.

Ha: there is a significant relationship between the amount of rainfall in an area and the quantity of air pollution removed.
45
Q

the Amount of rainfall (x) and quantity of air pollution removed (y)

correlation matrix p value is <.001

interpret

A

since the p value of correlation matrix is less than 0.05, we reject the Ho

46
Q

Ho of correlation matrix

A

there is NO correlation between x and y

47
Q

the Amount of rainfall (x) and quantity of air pollution removed (y)

pearson’s r value is -0.979

interpret

A

there is a strong, negative, and significant relationship between the amount of rainfall in an area and quantity of air pollution removed

48
Q

the Amount of rainfall (x) and quantity of air pollution removed (y)

r^2 is = 0.958

interpret

A

95.8% of the variablity in the quantity of air pollution removed is due to the variability in the amount of rainfall in an area

49
Q

the Amount of rainfall (x) and quantity of air pollution removed (y)

omnibus anova test p value = <.001

interpret

A

the model is signficant

50
Q

the Amount of rainfall (x) and quantity of air pollution removed (y)

intercept 153.175
amount of rainfall in an area -6.324

create a slope

A

y = 153 -6.324(amount of rainfall)

51
Q

the Amount of rainfall (x) and quantity of air pollution removed (y)

y = 153 -6.324(amount of rainfall)

interpret a

A

153.175 is the quantity of air pollution removed if the amount of rainfall in an area is zero

52
Q

the Amount of rainfall (x) and quantity of air pollution removed (y)

y = 153 -6.324(amount of rainfall)

interpret b

A

for every 1 unit increase in the amount of rainfall in an area, there is a 6.324 decrease in the quantity of air pollution removed

53
Q

the Amount of rainfall (x) and quantity of air pollution removed (y)

y = 153 -6.324(amount of rainfall)

how much pollution is removed if the amount of rainfall is 5.0?

A

y = 121.56 quantity of air pollution removed

54
Q

Correlation analysis is a measure of causal relationship between two variables

True
Neither true nor false
False
Sometimes true

A

False

55
Q

If the correlation coefficient is a positive value, then the slope of regression line must be

Either positive or negative
Negative
Neither negative nor positive
positive

A

positive

56
Q

If there exist a negative strong correlation between variables X and Y, then we can conclude that

The increase in X causes Y to decrease
The increases in X causes Y to increase
As the value of X increases, the value of Y decreases
As the value of X increases the value of Y also increases

A

as the value of x increases, the value of y decrease

57
Q

The correlation coefficient is used to determine

A specific value of the x-variable given a specific value of the y-variable
The strength of linear relationship between the x and y variables
A specific value of the y-variable given a specific value of the x-variable
The difference between the direction y-variable and x-variable

A

he strength of linear relationship between the x and y variables

58
Q

In regression, the equation that describes how the response variable (y) is related to the explanatory variable (x) is:

The correlation model
Used to compute the correlation coefficient
The regression model
The coefficient of determination mod

A

regression model

59
Q

In regression analysis, if the independent variable is measured in kilograms, the dependent variable

Must also be in kilograms
Cannot be in kilograms
Must be in some unit of weight
Can be any units

A

can be any units

60
Q

In regression analysis, the variable being predicted is the

Intervening variable
Independent variable
Response variable
Predictor variable

A

response variable

61
Q

The correlation coefficient is 0.8, and the percentage of variation in the response variable explained by the variation of the explanatory variable is

0.64%
64%
0.80%
80%

A

64%

62
Q

Which of the following values of correlation coefficient r show strong correlation

-0.91
0.525
0.01
1.0

A

-0.91

63
Q

If the coefficient of determination is 0.81, the correlation coefficient is

0.9 or -0.9
-0.651
90%
0.6561

A

0.9

64
Q

The study “Determinants of Board exam results in engineering” specifically aims to determine the linear relationship of Board Exam Score (BScore) and Entrance Exam Score in College (EScore). A correlation and regression analyses were used in the study an obtained the following results

Correlation analysis:

r= 0.924

Simple linear regression:
a= 25.17
b= 0.677

What is the estimate of the regression line?

EScore(y)=25.17+0.667Bscore(x)
EScore(y)=0.667+25.17BScore(x)
B Score(y)= 0.667+25.17Escore(x)
B score(y) = 25.17+0.667Escore(x)

A

B score(y) = 25.17+0.667Escore(x)

65
Q

A regression analysis between sales (in P1000) and price (in peso) resulted in the following equation: y(sales) = 50,000 - 8x(price). The above equation implies that an

Increase in P1 in price is associated with the decrease of P8000 in sale
Increase of P8 in price is associated with an increase of P8000 in sales
Increase of P1 in price is associated with a decrease of P8 in sales
Increase of P1 in price is associated with a decrease of P42,000 in sales

A

Increase in P1 in price is associated with the decrease of P8000 in sale

66
Q

The study “Determinants of Board exam results in engineering” specifically aims to determine the linear relationship of Board Exam Score (BScore) and Entrance Exam Score in College (EScore). A correlation and regression analyses were used in the study an obtained the following results

Correlation analysis:

r= 0.924

Simple linear regression:
a= 25.17
b= 0.677

Which of the given statements best described the correlation coefficient

There is a positive correlation between Escore and Bscore
There is a very strong correlation between Escore and Bscore
There is a very strong positive correlation between Escore and Bscore
There is a very strong linear relationship between Escore and Bscore

A

There is a very strong positive correlation between Escore and Bscore

67
Q

The study “Determinants of Board exam results in engineering” specifically aims to determine the linear relationship of Board Exam Score (BScore) and Entrance Exam Score in College (EScore). A correlation and regression analyses were used in the study an obtained the following results

Correlation analysis:

r= 0.924

Simple linear regression:
a= 25.17
b= 0.677

Which of the following best describe the slope of the regression line

The slope of the regression line suggest that a 1 unit increase in Bscore there is a 25.17 unit increase in E score
The slope of the regression line suggests that a 1 unit increase in Escore there is 25.17 unit increase in Bscore
The slope of regression line suggest that a 1 unit increase in the Bscore there is a 0.667 increse in Escore
The slope of the regression line suggests that 1 unit increase in the Escore that there is a 0.667 increase in Bscore

A

The slope of the regression line suggests that 1 unit increase in the Escore that there is a 0.667 increase in Bscore

68
Q

If there is a very strong correlation between two variables then the correlation coefficient must be

Much smaller than 0, if the correlation is negative
Much larger than 0, regardless whether the correlation is negative or positive
Very near to zero if the correlation is positive
Any value larger than 1

A

Much larger than 0, regardless whether the correlation is negative or positive

69
Q

Which of the following values of correlation coefficient r show weak correlation?

-1.0
0.11
0.89
-0.54

A

0.11

70
Q

Regression modeling is a statistical framework for developing a mathematical equation that describes how:

A. one response and one or more explanatory variables are related
B. one explanatory and one or more response variables are related
C. one response and one explanatory variables are related
D. several explanatory and several response variables response are related

A

one response and one or more explanatory variables are related

Biostatistics (10 decks)

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