Name ______

AP STATISTICS CHAPTER 3:

EXAMINING RELATIONSHIPS

A scatterplot :

The x variable is called the

The y variable is called the

We are looking for the and from the pattern.

To describe the overall pattern of a scatterplot, look for:

FORM:

DIRECTION:

STRENGTH:

An outlier falls .

Correlation measures the and of the relationship between two variables.

Correlation: r =

Facts about correlation ( r ):

“Facts” about r. Use your textbook and the video lesson to sniff out the false statements.

1. The correlation, r, takes on the unit of measurement of the explanatory (x-axis) variable. / 2. Changing units of x or y (like cm to inches, pounds to grams), will not change r. / 3. Positive r indicates a positive association between the variables.
4. The correlation is resistant. / 5. We can calculate r if x is a categorical variable, and y is a quantitative variable. / 6. In makes no difference which variable you call x and which you call y in calculating correlation.
7. Correlation will also take into account curved relationships. / 8. r values of +1 or -1 occur only when there is a perfect linear relationship. / 9. A value of r close to zero indicates a horizontal relationship.
10. Correlation is a complete description of two-variable data. / 11. A negative r-value indicates a weak association between the variables.


A REGRESSION LINE describes how a changes as an changes.

consider the following scatterplot.

The least-squares regression line makes the of the of the of the data points from the line .

Interpretations

Slope:

For each unit increase in x, there is an approximate increase/decrease of b in y.

Correlation coefficient:

There is a direction, strength, linear of association between x and y.

EQUATION OF THE LEAST-SQUARES LINE

Givens:

The equation is given by, where

y denotes .

denotes .

The following statistics are found for the variables posted speed limit and the average number of accidents.

.

Find the LSRL & predict the number of accidents for a posted speed limit of 50 mph.

Exercises:

Determine the correlation ( r ) for the following relationships. Write a sentence which describes the relationship.

Lengths of dinosaur bones
FEMUR / HUMERUS
38 / 41
56 / 63
59 / 70
64 / 72
74 / 84

Determine the least-squares line for the data sets above. Use a graphing calculator to find the statistics you need, assemble the equation, then use the LinReg features of your calculator to check.

Determine the correlation ( r ) for the following relationships. Write a sentence which describes the relationship.

Strength of concrete
DEPTH (mm) / STRENGTH
8.0 / 22.8
20.0 / 17.1
20.0 / 21.5
30.0 / 16.1
35.0 / 13.4
40.0 / 12.4
50.0 / 11.4
55.0 / 9.7
60.0 / 6.8

Determine the least-squares line for the data sets above. Use a graphing calculator to find the statistics you need, assemble the equation, then use the LinReg features of your calculator to check.

A RESIDUAL is the between an value of the response variable and the value by the .

Ex: The shoe sizes and heights (in inches) for 14 men. Use your calculator to determine the least-squares regression line. Then, determine the predicted value for each of the 14 men. Finally, calculate the residuals.

SHOE SIZE / HEIGHT / PREDICTED / RESIDUAL
8.5 / 66.0
9.0 / 68.5
9.0 / 67.5
9.5 / 70.0
10.0 / 70.0
10.0 / 72.0
10.5 / 71.5
10.5 / 69.5
11.0 / 71.5
11.0 / 72.0
11.0 / 73.0
12.0 / 73.5
12.0 / 74.0
12.5 / 74.0

A RESIDUAL PLOT is a scatterplot which compares the explanatory variable to the residuals. We can use a residual plot to help assess the fit of a regression line.

The coefficient of determination, r2, is the fraction of the in the values of y that is

by the of y on x.

A scatterplot comparing grade point averages and SAT scores is presented, with GPA’s being the explanatory variable. For this data, r2 is found to be .6502. Write a sentence which explains the meaning of this number.

For each of the following:

1) Compute appropriate statistics needed to find the least-squares regression equation.

2) Use formulas to find the regression equation, and write it in a descriptive manner.

3) Find r2, and write a sentence which explains its meaning in the context of the problem.

Problem 1: Is the number of games won by a major league baseball team related to its batting average? Before you begin, be sure you understand which variable is the explanatory and which is the response.

TEAM / GAMES WON / BATTING AVERAGE
NY / 87 / .277
TOR / 83 / .275
BALT / 74 / .272
BOS / 85 / .267
TB / 69 / .257
CLE / 90 / .288
DET / 79 / .275
CHI / 95 / .286
KC / 77 / .288
MIN / 69 / .270
ANA / 82 / .280
TEX / 71 / .283
SEA / 91 / .269
OAK / 91 / .270

An OUTLIER is .

An observation is INFLUENTIAL if .

Look for outliers in .

SUMMARY/QUESTIONS TO ASK IN CLASS