Take home test ch 3

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```					Chapter 3 Test                                                  Name: __________________________

True and False

1. _____The closer the absolute value of r is to one, the better will be the predictions made using
the equation of the line of best fit, provided the prediction is made for x values between the
smallest value of x and the largest value of x in the observed data.

2. _____In problems that deal with two quantitative variables, we will present the sample data
pictorially on a scatter diagram.

3. _____If the data points form a straight horizontal or vertical line, there is strong correlation.

4._____Although the correlation coefficient measures the strength of a linear relationship, it does
not tell us about the mathematical relationship between the two variables.

5._____ Perfect positive linear relationship occurs when all the points fall exactly above the
straight line.

6._____The primary purpose of linear correlation analysis is to measure the strength of a linear
relationship between two variables.

7._____ Correlation analysis is a method of obtaining the equation that represents the
relationship between two variables.

8. _____The linear correlation coefficient is used to determine the equation that represents the
relationship between two variables.

Multiple Choice

9. ______Select the most likely answer for the coefficient of linear correlation for the two
variables described below
x = the number of hours spent studying for a test, and
y = the number of points earned on the test
A. r = 1.20
B. r = 0.70
C. r = −0.85
D. r = 0.05

10._____ Select the most likely answer for the coefficient of linear correlation for the two
variables described below:
x = the weight, in pounds, of a college student, and
y = the grade point average for the student
A. r = 0.98
B. r = 0.65
C. r = 0.07
D. r = −0.65

I hereby claim that this is my work and only my work.

Name: ________________________________Signature: ___________________________________
Chapter 3 Test                                                Name: __________________________

11. ______Select the most likely value for the coefficient of linear correlation for the two
variables described below:
x = height in inches of college students, and
y = IQ’s of these college students
A. r = −0.87
B. r = 0.65
C. r = −0.02
D. r = 0.47

12. _____Suppose we used the equation, y = −2x + 3, to generate eight ordered pairs, (x, y). Then
using these ordered pairs to compute the coefficient of linear correlation, what value should we
expect to obtain for r?
A. +3
B. −1
C. +1
D. −2

13. ______A strong linear relationship exists between these two variables in the table (r = 0.97).
The equation of the least squares line is y\$ = 15.75− 0.55x. For what values of x should we use
this equation to make predictions?
x       5       7       8      10       11     12
y       5.5     8       8      9        10     11
A. Any positive value of x
B. Values of x less than or equal to 12
C. Values of x less than or equal to 5
D. Values of x between 5 and 12 inclusive

14. What difficulty is encountered in computing r for the following data?
x     1        2        3      4       5
y     6        6        6      6       6

________________________________________________________________________

15. What difficulty is encountered in computing r for the following data?
x     1        2        3      4       5
y     5        3        2      3       5

_______________________________________________________________________

_______________________________________________________________________

I hereby claim that this is my work and only my work.

Name: ________________________________Signature: ___________________________________
Chapter 3 Test                                                  Name: __________________________

16. For a particular set of bivariate data, the equation of the line of best fit isy\$ = −73.1+ 5.12x,
and y = 11.80. Find the value of x .

_________________________________________________

17. A student correctly computed the coefficient of linear correlation for two variables and
found the value to be r = −0.02. The student’s conclusion was that since the value of r is near
zero, the two variables are not related. Comment on this conclusion.
______________________________________________________________________

______________________________________________________________________

18. What is the main purpose of regression analysis?

____________________________________________________________________

19. A study investigating the relationship between speed (miles per hour) and gas rate (miles per
gallon) covered speeds ranging from 20 mph to 70 mph. Speed was the independent variable,
and gas rate was the dependent variable. The equation of the line of best fit was ˆy = 355 - 0.1x.
Estimate the average miles per gallon for cars of type tested traveling at 50 mph.

20. A survey of 15 doctors and 15 nurses was conducted, and one question related to their
smoking habit. The following coding was used: Doctor (D), Nurse (N), Smoker (S), Nonsmoker
(NS). The following results were obtained:
Respondent D          D      D       N     N      D       D      D       N       D
Smoking Habit S       NS      NS S         S      NS      NS     NS      S       NS

Respondent D              N        N       N        D   N      N       D       D       D
Smoking Habit NS          NS       S       NS       S   NS     NS      NS      NS      NS

Respondent    D      N       N       N      D       D          N       N       N       N
Smoking Habit NS     S       NS      NS S           S          NS      S       NS      NS
Summarize the data into a 2 × 2 cross-tabulation table.

I hereby claim that this is my work and only my work.

Name: ________________________________Signature: ___________________________________
Chapter 3 Test                                                   Name: __________________________

21. Consider the following bivariate data, extensions, and totals:
x        y       x2      xy      y2
2        14      4       28     196
3        13      9       39     169
4        11      16      44     121
5        8      25        40    64
5        9      25       45     81
7        4      49        28     16
7        3      49        21     9
33       62     177       245    656
Find the following:
a. SS(x) ________
b. SS(y)__________
c. SS(xy)____________
d. the linear correlation coefficient, r _____________
e. the slope, 1 b ______________
f. the y-intercept, 0 b ______________
g. the equation of the line of best fit _________________

22. Using the following bivariate data, find the equation of the line of best fit and use it to predict
the value of y when x = 7.
x       2       5      9      13
y       65     108     215    251

The predicted value of y when x is 7 is y = 155.5.

23. The following data were generated using the equation y = 2x + 3.
x        0       1     2       3       4
y       3       5      7       9       11
a. Draw a scatter diagram of these data. What did you notice?
b. Find the correlation coefficient and the equation of the line of best fit.

a.

b.

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Name: ________________________________Signature: ___________________________________

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