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Correlation, Linear Regression, Residuals Review

Total questions: 38

Worksheet time: 47mins

Name
Class
Date
1.

What is another name for the line of best fit?

Hint: There may be more than one answer.

a)

Linear regression

b)

Trend line

c)

Prediction line

d)

Fun line

2.
On a scatter plot, where can you find PREDICTED y-values?
a)
The data points
b)
On the regression line
3.
On a scatter plot, where can you find ACTUAL y-values?
a)
The data points
b)
On the regression line
4.
Which indicates a causal relationship?
a)
A rooster crowing and the sun rising
b)
Driving more miles and using more gas
c)
Eating salty food and buying a drink
d)
Going to the beach and building a sand castle
5.
Estimate the correlation coefficient.
a)
r = -0.8
b)
r = -0.5
c)
r = 0.5
d)
r = 0.8
6.
Shown is a residual plot. Would a linear regression model of the data be most appropriate?
a)
YES
b)
NO
7.
What should a residual plot look like?
a)
Distinct Pattern
b)
Curve
c)
Random
8.
As study time _______________, errors _______________.
a)
increases ; decrease
b)
increases ; increase
c)
decreases; decrease
d)
increases ; stays the same
9.
Shown is a residual plot.
Would a linear regression model be a good fit?
a)
YES
b)
NO
10.
This implies that one variable has a direct affect on the other variable.
a)
Correlation
b)
Causation
11.
A correlation shows that two things are
a)
related
b)
causing each other
c)
unrelated
12.
What is a line of best fit used for?
a)
To make predictions
b)
To make the graph look pretty
c)
To connect the points
13.
Which sentence describes the relationship shown on this scatterplot?
a)
As the temperature decreases, the visitors increase. 
b)
As the temperature increases, the number of visitors increases. 
c)
As the visitors increase, the temperature decreases. 
d)
No correlation
14.

Estimate the correlation coefficient for this scatterplot.

a)

r = -0.9

b)

r = 0.4

c)

r = 0.9

d)

r = -0.4

15.
Estimate the correlation coefficient for this scatterplot.
a)
r = 1.2
b)
r = 0.89
c)
r = 0
d)
r = -0.89
16.
The correlation coefficient is a number "r" such that: 
a)
-1<r<1
b)
-1>r>1
c)
-1≤r≤1
d)
-1≥r≤1
17.
r=0.3
a)
Strong positive 
b)
Weak positive
c)
Strong negative
d)
Weak negative 
18.
r=-0.89
a)
Strong positive 
b)
Weak positive 
c)
Strong negative 
d)
Weak negative 
19.
Which scatter plot shows a linear relationship between x and y?
a)
Graph A
b)
Graph B
c)
Graph C
d)
Graph D
20.
The scatter plot shows the relationship between the number of chapters and the total number of pages for several books. Use the trend line to predict how many pages would be in a book with 6 chapters. 
a)
100 pages
b)
170 pages
c)
60 pages
d)
20 pages
21.
What is the type of correlation?
a)
Negative 
b)
no association
c)
positive 
22.
What type of correlation describes the following sentence:
The temperature outside and the number of hot chocolate sold at a football game.
a)
postive
b)
negative 
c)
no
23.
A correlation shows that two things are
a)
related
b)
causing each other
c)
unrelated
d)
causation
24.

How do you calculate a residual?

a)

Actual value - Predicted value

b)

Predicted value - Actual value

c)

Actual value + Predicted value

d)

Predicted value + Actual value

25.

Residuals are . . .

a)

possible models not explored by the researcher

b)

variation in the response variable that is explained by the model

c)

the difference between the actual or observed response and the values predicted by the model

d)

data collected from individuals that is not consistent with the rest of the group

26.
Which is TRUE?
I.  Random scatter in the residuals indicates a linear model.
II.  If two variables are very strongly associated, then the correlation between them will be near 1 or -1.
III.  Changing the units of measurement for x or y changes the correlation coefficient.
a)
I only
b)
II only
c)
I and II only
d)
I, II and III
27.
After performing analyses on a set of data, Mrs. Schoeneck examined the scatter plot of the residual values for each analysis. Which scatter plot indicated the best linear fit for the data?
a)
A
b)
B
c)
C
28.

Which situation does not describe a causal relationship?

a)

The higher the volume on a radio, the louder the sound will be.

b)

The faster a student types a research paper, the more pages the paper will have.

c)

The shorter the distance driven, the less gasoline that will be used.

d)

The slower the pace of a runner, the longer it will take the runner to finish the race.

29.

Beverly did a study this past spring using data she collected from a cafeteria. She recorded data weekly for ice cream sales and soda sales. Beverly found the line of best fit and the correlation coefficient, as shown in the diagram.

Given this information, which statement(s) can correctly be concluded?

I. Eating more ice cream causes a person to become thirsty.

II. Drinking more soda causes a person to become hungry.

III. There is a strong correlation between ice cream sales and soda sales.

a)

I, only

b)

II and III

c)

I and III

d)

III, only

30.

What type of relationship exists between the number of pages printed on a printer and the amount of ink used by that printer?

a)

positive correlation, but not causal

b)

positive correlation, and causal

c)

negative correlation, but not causal

d)

negative correlation, and causal

31.

The table below shows the number of grams of carbohydrates, x, and the number of Calories, y, of six different foods.

Which equation best represents the line of best fit for this set of data?

a)

y = 15x

b)

y = 0.07x

c)

y = 0.1x − 0.4

d)

y = 14.1x + 5.8

32.

Analysis of data from a statistical study shows a linear relationship in the data with a correlation coefficient of -0.524. Which statement best summarizes this result?

a)

There is a strong positive correlation between the variables.

b)

There is a strong negative correlation between the variables.

c)

There is a moderate positive correlation between the variables.

d)

There is a moderate negative correlation between the variables.

33.

The results of a linear regression are shown.

Which phrase best describes the relationship between x and y?

a)

strong negative correlation

b)

strong positive correlation

c)

weak negative correlation

d)

weak positive correlation

34.

The table shows 6 students' overall averages and their averages in their math class.

If a linear model is applied to these data, which statement best describes the correlation coefficient?

a)

It is close to −1.

b)

It is close to 1.

c)

It is close to 0.

d)

It is close to 0.5.

35.

Which statistic would indicate that a linear function would not be a good fit to model a data set?

a)

r = −0.93

b)

r = 1

c)
d)
36.

After performing analyses on a set of data, Jackie examined the scatter plot of the residual values for each analysis. Which scatter plot indicates the best linear fit for the data?

a)
b)
c)
d)
37.
Which residual plot shows that a linear regression model would be most appropriate?
a)
a
b)
b
c)
c
38.
Base your answer to the following question on the following information. The table below displays the win/loss record of American League teams through 79 games in the 2006 season with the earned run averages of each team.
What is the correlation coefficient between wins and ERA?
a)
r = –0.66 
b)
r = –0.78
c)
r = –0.82
d)
r = –0.90

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