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Homework answers / question archive / 1)Consider the height and weight of 10 subjects given below

1)Consider the height and weight of 10 subjects given below

Math

1)Consider the height and weight of 10 subjects given below.  We seek to determine if there is a correlation between a person’s height and weight.

 

x=height (in)

69

71

70

67

75

66

71

71

67

65

y-weight (lbs)

151

159

163

153

198

126

163

185

133

140

 

 

 

 

  1.  Is there correlation?  If so is it positive or negative?  Is it strong or weak?

            

 

  1. Draw a line of best fit that goes through the points  ( 75, 198) and ( 70 ,  163 ) and find the equation of the line in slope intercept form (hint: y=mx+b)

 

 

  1.  What does the slope represent?

     
  2. Use your line of best fit to predict a person’s weight who is 68 inches tall

 

 

 

 

2.  A Math teacher is interested in studying the relationship between the level of stress before an exam and the score on the exam.  The following data gives the stress level and the students’ score on the exam

 

Stress test Score (x)

6.5

4

2.5

7.2

8

3.4

5.5

9

7.5

3.8

7

3

Final Exam score (y)

81

96

98

68

63

84

71

57

70

86

64

90

 

 

 

                  

 

 

(a)   Draw a line of best fit that goes through the points  (7.5,70) and (8,63).  Now let’s find the equation of the line in slope intercept form (hint: y=mx+b)

 

(b) What does the slope represent?

 

 

(C) Use your line of best fit to predict the final exam score for a student with a stress score of 10.

 

  1. A sample of seven households was obtained, and information on their income and food expenditures for the past month was collected.  The data (in hundreds of dollars) are:

 

Income ($100s) (x)

22

32

16

37

12

27

17

Food Expend ($100s) (y)

7

8

5

10

4

6

6

 

  1.   Make a scatterplot of the points using EXCEL

 

  1.   What is the correlation (positive, negative, neither)?

                                 

(c)    Find the equation of line of best fit that describes Income to Food Expenditures    (hint ) using EXCEL

 (d)    Write a sentence that interprets the estimated slope.

 

(e)    Use your line of best fit to predict the food expense for a family with $5200.

 

 

4.  The following table presents data on x= the number of oil changes per year and y = the cost of repairs for a sample of 10 cars from a given region:

 

Number of oil changes per year (x)

3

5

2

3

1

4

6

4

3

0

Cost of Repairs $ (y)

300

300

500

400

700

400

100

250

450

600

 

  1. Make a scatterplot of the points in EXCEL

 

  1. What is the correlation (positive, negative, neither)?

 

  1. Find the equation of line of best fit that describes the cost on the number of oil changes in EXCEL

 

 

 

(d)    Write a sentence that interprets the estimated slope.

 

  1. Use your line of best fit to predict the cost of car repairs for a car that had 7 oil changes per year.

 

 

5.   A student wonders whether people of similar heights tend to date each other.  She measures herself, roommate and 4 other girlfriends.  Then she measure the next man each woman dates.  (Heights are recorded in inches)

 

Height of Woman (x)

66

64

66

65

67

65

Height of Man (y)

72

68

70

68

72

67

 

(a)   Make a scatterplot of the points in EXCEL

 

(b)   What is the correlation (positive, negative, neither)?

 

 

  1. Find the line of best fit that describes the relationship between heights of Woman and Men.

 

(d)    Use your line of best fit to predict the height of a man if a woman were 50 inches.

 

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