Answer the
Answer the following questions using what you've learned from this unit. Write your responses in the space provided. Scoring: Each question is worth 5 points.
For questions 1 – 3, use the following scatterplot to answer the questions.
Use the following data set to answer questions 1 – 3:

1. Using the above scatterplot, does there seem to be a positive, negative, or no correlation between the number of ice cream cones sold and the daily high temperature?

2. Using the above scatterplot, what are the explanatory variable and the response variable?

3. Using the above scatterplot, what is a reasonable predicted number of ice cream cones sold for a daily temperature high of 95 degrees? Answer Choices:

explanatory variable: number of ice cream cones sold, response variable: temperature

Answer Choices:

Answer Choices: negative 500

none

600

positive

explanatory variable: hours of sunshine, response variable: number of ice cream cones sold

700

cannot tell with the given information 800

explanatory variable: number of ice cream cones sold, response variable: hours of sunshine explanatory variable: temperature, response variable: number of ice cream cones sold

For question 4, use the following scatterplot to estimate the correlation coefficient.

4. Estimate the correlation coefficient of the above scatterplot:
Answer Choices:
­0.89
­0.65
0.65
0.89 For questions 5­6, find the regression equation that best models the data shown in the table.
5.
x 0 1 2

3

4

5

6

7

y 2 6 1
2

1
7

3
6

7
2

13
8

27
5

y=32.976x­45.667

Calculation Tip: Using a graphing calculator, enter the x­values into one list and the y­values into another list, and then select the appropriate regression.
6.
x 0 1

2

3

4

5 6 7

y 8 1
3

1
4

1
5

1
1

9 6 2

y=­.655x^2+3.440x+9.167

For questions 7 – 8, use the following sets of data to calculate the correlation coefficient.
The data below show the mean swimming speed (m/s) of basking sharks of various sizes (m).

Length
(m)

Speed
(m/sec)

2.5

3

3.5

4.5

5

4.8

5.5

5.2

6

5.5

7. Use the above data to calculate the correlation coefficient.

8. Use the above data to interpret the correlation coefficient.

Answer Choices:

Answer Choices:

0.89

There is a very strong, positive, linear correlation between the mean length of basking sharks and their mean speed.

0.94 ­0.89
­0.94

There is a moderately strong, positive, linear correlation between the mean length of basking sharks and their mean speed.

There is a moderately strong, negative, linear correlation between the mean length of basking sharks and their mean speed. There is a very strong, negative, linear correlation between the mean length of basking sharks and their mean speed.

For questions 9 – 12, use the following data to calculate and interpret the following linear regression applications and assessment tools.
Percentages of public school students in 4th and 8th grade in 2008 who passed the California
State Assessment Test in Mathematics

Cities

4t h 8t h San Jose

32

62

Redding

45

71

Sacramento

36

62

San
Francisco

52

84

Los Angeles

29

61

San Diego

58

92

9. Calculate the linear regression equation from the above data.

10. What does the slope mean in context?

Answer Choices:
Answer Choices:
(8th grade pass rate) = 25.6 + 1.1 (4th grade pass rate)

For every 1% increase in 4th grade pass rate, the predicted 8th grade pass rate will increase by 25.6%.

(8th grade pass rate) = 1.1 + 25.6 (4th grade pass rate)

For every 1% increase in 8th grade pass rate, the predicted 4th grade pass rate will increase by 1.1%.

(4th grade pass rate) = 25.6 + 1.1 (8th grade pass rate)

For every 1% increase in 4th grade pass rate, the predicted 8th grade pass rate will increase by 1.1%.

(4th grade pass rate) = 1.1 + 25.6 (8th grade pass rate)

For every 1% increase in 8th grade pass rate, the predicted 4th grade pass rate will increase by 25.6%.

11. Using the table above, if Greentown had a
4th grade pass rate of 41% in 2008, what is the predicted pass rate for 8th grade?

12. Greentown had an actual 8th grade pass rate of 67%. What is the residual of this point using the equation you calculated from the data above?

Answer Choices:
Answer Choices:
49.8%
3.7%
52.5%
­3.7%
68.4%
6.4%
70.7%

­6.4%

For questions 13 – 17, use the following data to calculate and interpret the following linear regression applications and assessment tools.
Use the following data to answer questions 13 – 17:

x y
2

2
1

5

2
6

6

3
4

8

3
6

1
0

4
0

1
3

4
8

13. Construct a scatterplot of the above data. What does the scatterplot alone tell us about the relationship that exists between the variables x and y ?

14. Based only on looking at the scatterplot you constructed in problem
#13, what would you expect the correlation coefficient to be?

15. The linear regression equation and correlation coefficient from the above data was calculated to be:

Predicted y = 16.2 +
2.45( with x ) r = 0.98

Answer Choices:

Answer Choices:

They share a very strong, positive, linear correlation . They share a moderately strong, negative, linear correlation. r = ­0.98 r = ­0.72 r = 0.72 r = 0.98

What is the coefficient of determination? Answer Choices:
Coefficient of determination = 0.98

They share a very strong, negative, linear correlation. Coefficient of determination = 0.96

They share a moderately strong, positive, linear correlation. Coefficient of determination = 0.99

Coefficient of determination cannot be determined with only the given information.

16. The coefficient of determination calculated in problem #15 tells us what about the

17. Without calculating the residual plot, what would you expect to see? Specifically, using what you have discovered from

linear regression model calculated using the above data?

looking at a scatterplot of the data and discovering the correlation coefficient and coefficient of determination, what kind of pattern should you see in a residual plot using this data set?

Answer Choices:

The linear regression equation will be a good model used to predict values. y ­

Answer Choices:

The linear regression equation will be a poor model used to predict values. y ­ The linear regression equation will be a good model used to predict values. x ­ The linear regression equation will be a poor model used to predict values. x ­

The residual plot should show a random and scattered pattern. The residual plot should show a clear pattern or curve. The residual plot should show a positive linear pattern. You cannot tell without looking at the residual plot.

For questions 18 – 20, use the following data to calculate and interpret the following linear regression applications and assessment tools.
Use the following data set to answer questions 18 – 20:

x

y

1

2

3

9

4

15

6

50

8

258

1
0

123
6

18. Transform the data. Take the log( , and calculate y ) the linear regression equation and correlation coefficient of the transformed data.
Specifically, find the linear regression equation of log( and y ) x .

19. Transform the data. Take the log( and log( , and y ) x ) calculate the linear regression equation and correlation coefficient of the transformed data.
Specifically, find the linear regression equation of log( in y ) terms of log( . x )

20. Use the best fit (the equation from either problem #18 or problem
#19, whichever one is a better fit) to predict y when = 12. x Answer Choices:

3.64

Answer Choices:
Answer Choices: log( = ­0.023 + 0.305 ( , y ) x ) with r = 0.998

2456 log( = ­0.023 + 0.305 y ) log( , with x ) r = 0.998

4335

5687

log( = 0.305 ­ 0.023 ( , y ) x ) with r = 0.998

log( = 0.305 ­ 0.023 y ) log( , with x ) r = 0.998

log( = ­359.02 + 116.4 y )
( , with x ) r = 0.795

log( = ­ 0.04 + 2.62 y ) log( , with x ) r = 0.933

log( = 1116.4 ­ 3359.02 y )
( , with x ) r = 0.795

log( = 2.62 ­ 0.04 log( , y ) x ) with r = 0.933

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