Chapter 3 - Scatterplots and Correlation

Question 0

-may help explain or predict changes in a response variable;
-goes on the x axis of a graph
ex- car weight and number of cigarettes smoked

Answer 0

explanatory variable

Question 1

-measures an outcome of a study;
-goes on the y variable of a graph
ex- accident death rates and life expectancies

Answer 1

response variable

Question 2

-shows relationship between two quantitative variables measured on the same individuals;
ex- percent of students taking the sat & the mean math score

Answer 2

scatter plot

Question 3

how to describe a scatter plot

Answer 3

Identify DCFS

direction
correlation
form
strength

Question 4

when above average values of one variable tend to accompany above average values of the other and when below average values occur together

Answer 4

positive association

Question 5

when above average values of one tend to accompany below average values of the other

Answer 5

negative association

Question 6

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

Answer 6

correlation

Question 7

value between -1 and 1

Answer 7

correlation (r)

Question 8

r>0

Answer 8

positive association

Question 9

r<0

Answer 9

negative association

Question 10

interpreting correlation

Answer 10

• correlation makes no distinction between explanatory and response variables
• r does not change when we change the unit of measurement of x, y, or both
• correlation does not equal causation
• both variables need to be quantitative
• correlation is not resistant: r is affected by outliers

Question 11

determined by how close the points in the scatter plot lie

Answer 11

strength

Question 12

• points show a straight line pattern

- watch out for curved relationships and clusters

Answer 12

form

Question 13

• summarizes the relationship between two variables when one of the variables helps explain or predict the other
• requires explanatory and response variable
• describes how variable y changes as variable x changes
• used to predict value of y for a given value of x

Answer 13

regression line

Question 14

regression line

Answer 14

y hat = a+bx

Question 15

in y hat=a+bx

y hat is the ____

Answer 15

predicted value of the response variable y for a given value of the explanatory variable x

Question 16

in y hat=a+bx

b represents ____

Answer 16

slope

Question 17

in y hat=a+bx

a is the ____

Answer 17

y intercept;

predicted value of y when x=0

Question 18

coefficient of x is always the ____, no matter what symbol is used

Answer 18

slope

Question 19

use of regression line for prediction far outside the interval of values of the explanatory variable to obtain the line

Answer 19

extrapolation

Question 20

difference between observed value of the response variable and the value predicted by the regression line;
residual = observed y - predicted y
=y - y hat

Answer 20

residual

Question 21

if after adding up the predictions, the positive and negative residuals cancel out you should..

Answer 21

square the residuals

Question 22

• y on x

- line that makes the sum of the squared residuals as small as possible

Answer 22

least squares regression line

Question 23

the mean of the least squares residuals is always ____

Answer 23

zero

Question 24

- scatter plot of the residuals against the explanatory variable - help us assess whether a linear model is appropriate

Answer 24

residual plot

Question 25

turns the regression line horizontal

Answer 25

residual plot

Question 26

find form of a residual plot

Answer 26

form of residual plot = form of association - form of model

Question 27

- gives the approximate size of a typical prediction error (residual) - use least squares regression line to predict the values of a response variable y from an explanatory variable x

Answer 27

standard deviation of the residuals (s)

Question 28

- coefficient of determination - predicts values of the response variable y - fraction of the variation in the values of y that is accounted for by the least squares regression line of y on x

Answer 28

r^2

Question 29

relationship between the standard deviation of the residuals (s) and the coefficient of determination r^2

Answer 29

- both calculated from sum of squares residuals | - assess how well the line fits the data

Question 30

how to calculate least squares regression line

Answer 30

-calculate means x and y and the standard deviations sx and sy and their correlation r b=r(sy/sx)

Question 31

when the correlation isn't r=1 or -1, the predicted value of y is closer to It's mean y bar than the value of x is to It's mean x bar

Answer 31

regression to the mean; | values of y "regress" to their mean

Question 32

least squares regression lines are not ____

Answer 32

resistant

Question 33

points that are outliers in the __ direction but not the __ direction of a scatter plot have large residuals

Answer 33

y, x

Question 34

an observation is ____ for a statistical calculation of removed it would change the result of the calculation

Answer 34

influential

Question 35

how to verify that a point is influential

Answer 35

find the regression line both with and without questionable point