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Holt McDougal Algebra 1

3-4 Graphing Functions

You will determine correlation of a scatter plot and real world situation.

You will find a trend line for a scatter plot (line of best fit)

You will determine if a graph or statement represents correlation or causation.

You will interpret the correlation coefficient for a line of best fit.



Example 2: Describing Correlations from Scatter

Plots

Describe the correlation illustrated by the scatter plot.

There is a positive correlation between the two data sets.

As the average daily temperature increased, the number of visitors increased.

a. Positive correlation

b. Negative correlation

c. No correlation



Check It Out! Example 2

Describe the correlation illustrated by the scatter plot.

There is a positive correlation between the two data sets.

As the years passed, the number of participants in the snowboarding competition increased.



c. No correlation



Example 3A: Identifying Correlations

the average temperature in a city and the number of speeding tickets given in the city

You would expect to see no correlation. The number of speeding tickets has nothing to do with the temperature.

Identify the correlation you would expect to see between the pair of data sets. Explain.



c. No correlation



the number of people in an audience and ticket sales

You would expect to see a positive correlation. As ticket sales increase, the number of people in the audience increases.

Example 3B: Identifying Correlations




c. No correlation



a runner’s time and the distance to the finish

line

You would expect to see a negative correlation. As time increases, the distance to the finish line decreases.

Example 3C: Identifying Correlations




c. No correlation



Example 4: Matching Scatter Plots to Situations

Choose the scatter plot that best represents the relationship between the age of a car and the amount of money spent each year on repairs. Explain.

Graph A Graph B Graph C



Example 5: Fund-Raising Application

The scatter plot shows a relationship between the total amount of money collected at the concession stand and the total number of tickets sold at a movie theater. Based on this relationship, predict how much money will be collected at the concession stand when 150 tickets have been sold.

Draw a trend line and use it to make a prediction.

Draw a line that has about the same number

of points above and below it. Your line may or

may not go through data points.

Find the point on the line whose x-value is

150. The corresponding y-value is 750.

Based on the data, $750 is a reasonable prediction of how much money will be collected when 150 tickets have been sold.



Check It Out! Example 5

Based on the trend line, predict how many wrapping paper rolls need to be sold to raise $500.

Is this an example of interpolation or extrapolation?

Find the point on the line whose

y-value is 500. The corresponding

x-value is about 75.

Based on the data, about 75 wrapping paper rolls is a reasonable prediction of how many rolls need to be sold to raise $500. Interpolation



The scatter plot shows the number of orders placed for flowers before Valentine’s Day at one

shop. Draw a trend line. Based on this relationship, predict the number of flower orders placed on February 12. Is this an example of interpolation or extrapolation?

about 45; extrapolation



Correlation VS Causation

Is it possible to have correlation without causation?

What does correlation mean?

What does causation mean?



Correlation is used in statistics to represent the strength and

direction of a linear relationship between two random variables. A

scatter plot is a graphical representation of data that shows

different types of correlations. Sometimes the correlation between

two events can seem directly linked, but in reality, the two situations

do not impact each other.

Causation is a link between variables so that a change in one

variable is believed to produce the change in the other variable.

A correlation between two variables does not imply a causation.

It is possible that a common, outside factor, called a confound,

might produce the relationship indicated by the strong

correlation.



Correlation?

a. Positive

b. Negative

c. none



Causation?

a. Yes

b. No



Which statement is true about the graph?

a. People tend to marry someone around their own age

b. As a husband gets older, they marry younger

c. As a wife gets older they marry younger?

d. None of these



The number of members in a family and the size of the family’s grocery bill.



c. No correlation

Causation?????



The temperature in Houston and the number of cars sold in Boston.



c. No correlation



Correlation?

The number of students enrolled in a class and the number of empty seats in the classroom.

a. Positive

b. Negative

c. No correlation





c. No correlation



Which is true about fish swimming speeds?

a. The shorter the fish, the faster they swim

b. The longer the fish, the faster they swim

c. There is no link between fish length and speed



Which line represents the best line of best fit for the data?

a. Blue

b. Green

c. red



Based on the line of best fit, predict the score of a student who studies for 10 hours.



The Correlation Coefficient, denoted by the letter r, is a number

from -1 to 1 that measures the strength and direction of the

correlation between two variables. It is used to measure the

“goodness” of the fit line.

The mathematical formula for computing r is:

where n is the number of pairs of data.(But don’t worry; we will use a graphing calculator instead).



Which of the following correlation coefficients would indicate a strong negative relationship between the number of text messages sent and the age of the sender?

a. -0.95

b. -0.82

c. 0.05

d. 0.28



The correlation coefficient that models the relationship between the

amount of time Jason spends working out and the amount of weight

he loses is -0.9547. What is the correct interpretation of this number?a. The correlation coefficient is close to 0. There is a weak positive correlation

between the amount of time spent working out and the amount of weight

lost.

b. The correlation coefficient is close to -1. There is a weak negative correlation

between the amount of time spent working out and the amount of weight

lost.

c. The correlation coefficient is close to -1. The correlation between the

amount of time spent working out and the amount of weight lost cannot be

determined.

d. The correlation coefficient is close to -1. There is a strong negative

correlation between the amount of time spent working out and the amount

of weight lost.



What type of correlation would you expect between a

company’s advertising budget and its volume of sales?

Why?

a.0; relatively no correlation

b.The correlation cannot be predicted

c. Positive; advertising increases, sales increase.

d.Negative; fewer sales, less money for advertising.



Victor, Vladimir, Venus, and Vivian each have a different set of data points.

Each used the linear regression feature of the graphing calculator to find a

linear function that models his/her data.

The value of the correlation coefficient (r) associated with Victor’s function

was -0.91, the value or r for Vladimir’s function was 0.73, the value of r for

Venus’s function was -0.44, and the value of r for Vivian’s function was

0.88.

Who has the BEST model for his or her data?

a. Venus

b. Victor

c. Vivian

d. Vladimir



The graph shows a correlation between the number of civil engineering doctorates awarded and the number of pounds of mozzarella cheese consumed.

Does this mean that civil engineer doctorates CAUSE mozzarella consumption to increase?



The graph represents:

a. Correlation

b. Causation



When determining statements of causation, remember that causation is represented by a DEFINITE statement.

Choose all that apply.



Which quantities are most likely to

have a cause-and-effect relationship?a. The average number of televisions per

household in a country and the country’s

average life expectancy.

b. A student’s grade in history class and the

student’s grade in math class.

c. The level of nutrients in soil and the rate of

plant growth

d. The amount of ice cream sold and the number

of people wearing sunglasses.

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