Chapter 3 Describing Relationships

Question 1

response variable

Answer 1

measures an outcome of a study

Question 2

explanatory variable

Answer 2

may help explain or influence changes in a response variable

Question 3

scatter plot

Answer 3

shows the relationship between two quantitative variables measured on the same individuals, the values of one variable appear on the horizontal axis, and the values of the other variable appear on the vertical axis, each individual in the data appears as a point as a point in the graph

Question 4

how to make a scatter plot

Answer 4

1. decide which variable should go on each axis. 2. label and scale your axis. 3. plot individual data values

Question 5

positive association

Answer 5

in two variables, when above average values of one tend to accompany above average values of the other, and when below average values also tend to occur together

Question 6

negative association

Answer 6

in two variables, when above average values of one tend to accompany below average values of the other

Question 7

correlation r

Answer 7

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

Question 8

regression line

Answer 8

is a line that describes how a response variable y changes as an explanatory variable x changes. they are often used to predict the value of y for a given value of x

Question 9

“y hat”

Answer 9

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

Question 10

slope (b)

Answer 10

the amount by which y is predicted to change when x increase by one unit

Question 11

y-intercept (a)

Answer 11

the predicted value of y when x=0

Question 12

extrapolation

Answer 12

the use of regression line for prediction far outside the interval of values of the explanatory variable x used to obtain the line, some prediction are often not accurate

Question 13

residual

Answer 13

the difference between an observed value of the response variable and the value predicted by the regression line

Question 14

least-square regression line of y on x

Answer 14

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

Question 15

residual plot

Answer 15

a scatter plot of the residuals against the explanatory variable, they help us access how well a regression line fits the data

Question 16

the coefficient of determination: r^2 in regression

Answer 16

the fraction of the variation in the values of y that is accounted for by the least-squares regression line of y on x

Question 17

outlier

Answer 17

an observation that lies outside the overall pattern of the other observations. points in the y direction but not the x direction of the scatter plot have large residuals

Question 18

influential observations in regression

Answer 18

if removing it would markedly change the result of the calculation, points that are outliers in the x direction of a scatterplot are often influential for the least-squares regression line