Ch 3 Flashcards
Response variable
measures an outcome of a study
explanatory variable
may explain or predict changes in a response variable
x and y ?
response is y
explanatory is x
ex. blood alcohol levels and cans of beer
response- blood alcohol levels
explanatory- cans of beer
Scatter plot
shows the relationship between 2 quantitative variables
describe a scatter plot?
direction - positive/negative
strength - strong/weak
form - linear/non-linear
What does R measure?
the direction and strength of a linear relationship
- correlation coefficent
correlation R is always between?
1 and -1
what is the weakest and what is the strongest collection of r?
0 - weakest
-1 and 1 - strongest
how can you tell the direction from r?
direction by the sign
- = negative correlation
how to find r on your calculator?
stats, calculations, linear regression (#4)
what does the correlation of zero imply?
there is no LINEAR relationship
is a correlation a complete summary of 2 variable data?
no
is the correlation more like the mean or median in relation to sensitivity?
more like the mean, it is not resistant and is sensitive to outliers
true or false, a value of r close to 1 or -1 guarantees a linear relationship between 2 variables
false
what does r collection only measure?
only linear, it does not describe curved relationships between variables
what does correlation require?
requires both variables to be quantitative
Are relationships in correlations always cause and effect?
no, correlation does NOT imply causation
does r have a unit?
NEVER , r itself has no unit of measure
true or false, r does not change when we change the units of measure of x, y, or both
TRUE
Regression line
(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.
Regression line is also known as?
Line of best fit
Model for the data (like a density curve)
Regression line equation
Regression line relating y to x has the equation
Predicted y= a+bx
What is y hat
Predicted y value
Predicted value of response variable y for a given explanatory variable x.
What is b?
B is the slope, amount by which y is predicted to change when x increases by 1 unit.
What is a?
The y intercept, predicted value of y when x=0.
Residual
Difference between an observed (actual) value of the response variable & the value predicted by the regression line.
R=A-P
Least-squares regression line
Y on x is the line that makes the sum of squared residuals as small as possible
MINIMIZES THE RESIDUALS
Residual plot
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
What are 2 ways to determine if our model is good?
Standard deviation of the residuals (s)
Coefficient of determination (r^2)
What does s tell us? When do we use it?
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)
What is r^2?
R^2 % of the variation in response variable is explained by the linear relationship between response variable and explanatory variable.
