Ch 3

Question 1

Response variable

Answer 1

measures an outcome of a study

Question 2

explanatory variable

Answer 2

may explain or predict changes in a response variable

Question 3

x and y ?

Answer 3

response is y

explanatory is x

Question 4

ex. blood alcohol levels and cans of beer

Answer 4

response- blood alcohol levels

explanatory- cans of beer

Question 5

Scatter plot

Answer 5

shows the relationship between 2 quantitative variables

Question 6

describe a scatter plot?

Answer 6

direction - positive/negative
strength - strong/weak
form - linear/non-linear

Question 7

What does R measure?

Answer 7

the direction and strength of a linear relationship

- correlation coefficent

Question 8

correlation R is always between?

Answer 8

1 and -1

Question 9

what is the weakest and what is the strongest collection of r?

Answer 9

0 - weakest

-1 and 1 - strongest

Question 10

how can you tell the direction from r?

Answer 10

direction by the sign

- = negative correlation

Question 11

how to find r on your calculator?

Answer 11

stats, calculations, linear regression (#4)

Question 12

what does the correlation of zero imply?

Answer 12

there is no LINEAR relationship

Question 13

is a correlation a complete summary of 2 variable data?

Answer 13

no

Question 14

is the correlation more like the mean or median in relation to sensitivity?

Answer 14

more like the mean, it is not resistant and is sensitive to outliers

Question 15

true or false, a value of r close to 1 or -1 guarantees a linear relationship between 2 variables

Answer 15

false

Question 16

what does r collection only measure?

Answer 16

only linear, it does not describe curved relationships between variables

Question 17

what does correlation require?

Answer 17

requires both variables to be quantitative

Question 18

Are relationships in correlations always cause and effect?

Answer 18

no, correlation does NOT imply causation

Question 19

does r have a unit?

Answer 19

NEVER , r itself has no unit of measure

Question 20

true or false, r does not change when we change the units of measure of x, y, or both

Answer 20

TRUE

Question 21

Regression line

Answer 21

(Line of best fit)
Line that describes how a response variable y changes as an explanatory variable x changes, often use a regression line to predict the value of y for a given value x.

Question 22

Regression line is also known as?

Answer 22

Line of best fit

Model for the data (like a density curve)

Question 23

Regression line equation

Answer 23

Regression line relating y to x has the equation

Predicted y= a+bx

Question 24

What is y hat

Answer 24

Predicted y value

Predicted value of response variable y for a given explanatory variable x.

Question 25

What is b?

Answer 25

B is the slope, amount by which y is predicted to change when x increases by 1 unit.

Question 26

What is a?

Answer 26

The y intercept, predicted value of y when x=0.

Question 27

Residual

Answer 27

Difference between an observed (actual) value of the response variable & the value predicted by the regression line.
R=A-P

Question 28

Least-squares regression line

Answer 28

Y on x is the line that makes the sum of squared residuals as small as possible
MINIMIZES THE RESIDUALS

Question 29

Residual plot

Answer 29

Scatter plot of the residuals against the explanatory variable, helps us assess whether a linear model is appropriate
- appropriate if plot shoes no pattern, random scatter

Question 30

What are 2 ways to determine if our model is good?

Answer 30

Standard deviation of the residuals (s)

Coefficient of determination (r^2)

Question 31

What does s tell us? When do we use it?

Answer 31

When using the LSRL to predict response variable, we will typically be off by ___(s)_____.
S gives us ~ size of a “typical” prediction error
(How far away from actual data)

Question 32

What is r^2?

Answer 32

R^2 % of the variation in response variable is explained by the linear relationship between response variable and explanatory variable.