AP Stat Ch 3 and 12.2

Question 0

Explanatory variable

Answer 0

Attempts to explain or influence changes in a response variable.
Independent variable. X axis

Question 1

Response variable

Answer 1

Measures an outcome of a study.

Dependent variable

Question 2

Which is explanatory variable:

1. Scuba diving: depth and visibility
2. World population vs. year
3. Amount of rain vs. crop growth
4. Height vs. GPA

Answer 2

1. Depth
2. Year
3. Amount of rain
4. No association

Question 3

Scatter plot

Answer 3

The most effective way to display the relation between two quantitative variables measured on the same individuals.

Question 4

Tips for drawing scatterplot by hand

Answer 4

1. Plot explanatory variable on x axis
2. Label both axes
3. Scale the axes with uniform intervals
4. Make plot large enough to see details

Question 5

Four major features in interpreting scatter plots

Answer 5

Direction
Form
Scatter
Outliers

Question 6

Direction

Answer 6

A pattern from the upper left to the lower right is said to have a negative direction. A pattern from lower left to upper right has a positive direction.

Question 7

Form

Answer 7

Approx linear, curved, exponential…

Question 8

Scatter

Answer 8

Strength of relationship.

Strong to weak on a scale

Question 9

Positive vs negative association

Answer 9

Positive when above average values of one tend to accompany above average values of other. Slope is positive.
Negative when above average with one accompanies below average of the other variable. Negative slope

Question 10

Correlation

Answer 10

The correlation, r, is a common measure used to numerically asses the association between two quantitative variables. Measures the direction and strength of a linear relationship. On a scale of -1 to 1.
Indicates direction by its sign and strength by how far r moves away from 0.
Obtained from stat menu, Calc, 8.
Don’t need to calculate by hand, but it is sum of the standard deviations of x times the sum of the standard deviations of y divided by n-1

Question 11

What happens as r gets closer to 0

Answer 11

Weaker

Stronger as further from zero

Question 12

Properties of r

Answer 12

1. No units
2. Doesn’t depend on which variable is x and y as product of scores of x times y is same as y times x.
3. Correlation requires both variables to be quantitative
4. -1<= r => 1
   When r is greater than zero, relationship is positive.
   When r less than zero, relationship negative
5. r only =1 or -1 when the data is perfectly linear.
6. Value of r is a measure of the strength of a linear relationship only. Measures how closely the data fall into a straight line. R value near zero doesn’t indicate no relationshop, but rather, no linear relation.
7. Not resistant.

Question 13

Don’t confuse correlation with causation

Answer 13

Just because number of students taking stat has increased and murders are down, doesn’t mean that one causes the other

Question 14

Regression line

Answer 14

A line that describes how a response variable y changes as an explanatory variable x changes. We often use a regression line to predict the value of y for a given value of x.
Stat Calc 8
LRSL- least squares regression line
Y hat = a + bx

Question 15

LSRL form

Answer 15

Y hat = a + bx
A is the y intercept
B is the slope
Y hat is used as a prediction of the model
When interpreting the slope, always mention according to the Model, as x increases by one, the y variable is expected to increase by b.

Question 16

Extrapolation

Answer 16

Predict based on ref line outside data domain. DO NOT EXTRAOLATE EVER

Question 17

Residuals

Answer 17

The difference between an observed value of the response variable and the value predicted by the regression line. The vertical distance from the point to the line.
Y minus y hat

Question 18

What does it mean when residual is pos/neg?

Answer 18

When pos, y is greater than y hat. So value above prediction, above LSRL
when neg, y is less than y hat. So value below prediction, below LSRL.

Question 19

Important questions to consider with LSRL

Answer 19

1. Is linear model really appropriate, or would curved model be better
2. Are there any unusual aspects of the data set?
3. If we make predictions, how accurate?

Question 20

Residual plot

Answer 20

Scatterplot of the regression residuals against the explanatory variable. If there is a pattern then it shows that linear is not the best model

Question 21

If an observation has a positive residual, then…

Answer 21

Y minus y hat is positive. So y is above the expected value. So y is above the line. The prediction is too low.

Question 22

If an observation has a negative residual, then…

Answer 22

Y minus y hat is negative, so y hat is larger. This means that the predicted value is too high. We are below the predicted value

Question 23

Only way to tell you if a linear model is the best choice…

Answer 23

RESIDUAL PLOT PATTERN!

Question 24

Standard deviation about least squares regression line

Answer 24

Shows you how close the observation is to the line. The approximate size of a typical or average prediction error (residual). Represented by S. If S= 4 UNITS (same as y), shows that the typical deviation from the expected value is 4 units.

Question 25

Coefficient of determination (r squared)

Answer 25

r squared is a measure of the proportion of variability in the y variable that can be explained by the linear relationship between x and y. Also tells u how well the LSRL is at predicting values of y. Say that r squared = .74 (no units). 74% of the variability in army attririgbted to years of experience. Or that the LSRL is 74% better at predicting y than using the mean y value every time.

Question 26

How to get r from r squared

Answer 26

SQRT and then positive if slope is pos and negative if slope is neg.

Question 27

Correlation and regression describe only...

Answer 27

LINEAR RELATIONSHIPS

Question 28

Is correlation resistant?

Answer 28

No!

Question 29

Outlier

Answer 29

Observation that lies outside the overall pattern of the other observations.

Question 30

Influential point

Answer 30

An observation is influential if removing it would markedly change the result of the calculation. Points that are outliers in the direction scatter plot are oftne influential.

Question 31

Influential points and outlier relationship

Answer 31

An influential points is always an outlier. | An outlier not always influential.

Question 32

Lurking variable

Answer 32

Variable not among the explanatory or response variables in a study and yet may influence the interpretation of relationships among those variables.

Question 33

Summary of chapter 3:

Answer 33

1. Graph data 2. Generate LSRL 3. R tells us how well the data fits the line--correlation, desire whether this is the most appropriate model 4. Residual plot tells us whether a linear model is appropriate. 5. S tells us our average error if/when we use LSRL to predict Y 6. R squared tells us how much better our LSRL is at predicting our y value than using the mean y value every time. Also explains the percent of variability in y as x changes

Question 34

Exponential models

Answer 34

Take ln or log of just the y variable Then solve for y hat. a * b^x

Question 35

Base of exponential function

Answer 35

In form a*b^x B will be positive. 1+/- r For example, if b=1.057, then y hat is increasing 5.7% for every one increase in x If b= .79, then y hat is decreasing 21% for every one increase in x When b is less than one, decrease. Greater is increasing

Question 36

Power model

Answer 36

Take log or ln of both x and y a*x^b As x increases by 1, y will increase by 1/b