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Math | Graded Assignment | Unit Test, Part 2 | Relationships Between Variables Name: Date: Graded Assignment Relationships Between Variables Answer the questions below. When you have finished, submit this assignment to your teacher by the due date for full credit. Total score: ____ of 24 points (Score for Question 1: ___ of 12 points) The table shows the life expectancy of females and males in a sample of 10 countries. Country Female Male India 64 62 Norway 82 77 Bolivia 66 62 Ghana 59 58 Austria 82 76 South Africa 56 51 United Kingdom 81 76 Myanmar 63 57 China 74 70 Panama 77 72 (a) Create a scatter plot for the data on the grid. Identify any clusters or outliers. © 2015 K12 Inc. All rights reserved. Copying or distributing without K12’s written consent is prohibited. Page 1 of 4 Math | Graded Assignment | Unit Test, Part 2 | Relationships Between Variables (b) Use technology to find the equation of the least squares regression line, the correlation coefficient, and the coefficient of determination. Round each to three decimal places. Sketch the line in the scatter plot. Interpret the correlation coefficient and the coefficient of determination. (c) Use the equation of the least squares regression line to predict the male life expectancy in Egypt, where the female life expectancy is 72. Round to one decimal place. Answer: © 2015 K12 Inc. All rights reserved. Copying or distributing without K12’s written consent is prohibited. Page 2 of 4 Math | Graded Assignment | Unit Test, Part 2 | Relationships Between Variables (Score for Question 2: ___ of 8 points) A company manager found the number of vacation days available and the number of vacation days taken during one year for a sample of employees as shown in the table. The equation of the regression line is y = 0.8 x − 0.47 . (a) Complete the table by finding the predicted and residual values. Round to one decimal place. Vacation Days Available x Vacation Days Taken y 7 6 14 10 6 3 21 15 18 15 10 10 10 6 18 14 8 5 12 10 Predicted Days Taken y Residual e (b) Create a residual plot for the data set on the grid below. (c) Explain whether a linear regression line is a good fit for the data set. Answer: © 2015 K12 Inc. All rights reserved. Copying or distributing without K12’s written consent is prohibited. Page 3 of 4 Math | Graded Assignment | Unit Test, Part 2 | Relationships Between Variables (Score for Question 3: ___ of 4 points) Answer the following. (a) The owner of an ice-skating rental company heard that ice-skate rentals are predicted to increase a whopping 50% this year over last year. Explain why the number of increases might not be quite as whopping as it sounds. (b) The owner also heard that ice-skate rentals tend to increase or decrease as hot chocolates sales increase or decrease. The owner is fairly sure that ice skating doesn't make people crave hot chocolate, nor does drinking hot chocolate make people want to ice skate. What is the most likely lurking variable? Explain. Answer: © 2015 K12 Inc. All rights reserved. Copying or distributing without K12’s written consent is prohibited. Page 4 of 4

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TabbyK
School: UCLA

Uploading after finishing each part.

Math | Graded Assignment | Unit Test, Part 2 | Relationships Between Variables

Name:

Date:

Graded Assignment
Relationships Between Variables
Answer the questions below. When you have finished, submit this assignment to your teacher by the due date for
full credit.
Total score: ____ of 24 points
(Score for Question 1: ___ of 12 points)

The table shows the life expectancy of females and males in a sample of 10 countries.
Country

Female

Male

India

64

62

Norway

82

77

Bolivia

66

62

Ghana

59

58

Austria

82

76

South Africa

56

51

United Kingdom

81

76

Myanmar

63

57

China

74

70

Panama

77

72

(a) Create a scatter plot for the data on the grid. Identify any clusters or outliers.
A scatter plot for the data is as follows:

© 2015 K12 Inc. All rights reserved.
Copying or distributing without K12’s written consent is prohibited.

Page 1 of 6

Math | Graded Assignment | Unit Test, Part 2 | Relationships Between Variables

Male and Female life expectancy

(b) Use technology to find the equation of the least squares regression line, the correlation coefficient,
and the coefficient of determination. Round each to three decimal places. Sketch the line in the
scatter plot. Interpret the correlation coefficient and the coefficient of determination.
The equation of the least squares regression line is sketched as follows:

© 2015 K12 Inc. All rights reserved.
Copying or distributing without K12’s written consent is prohibited.

Page 2 of 6

Math | Graded Assignment | Unit Test, Part 2 | Relationships Between Variables

The equation is y = 0.9216x + 1.2188, where y = male life expectancy and x = female life expectancy.
The correlation coefficient from excel calculations is 0.988
The coefficient of determination is 0.976 from excel analysis.
Interpretation: The correlation coefficient measures the linear relationship between male life expectancy
and female life expectancy. A correlation coefficient of 0.988 shows a positive and very relationship between male
life expectancy and female life expectancy. In this regard, an increase in the male life expectancy is accompanied
by an increase in female lif...

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Anonymous
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