# Graphical Relationship – Discussion Week 3

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## Sheet1

AGE | Smoker | PULSE | HDL | LDL | WEIGHT | HEIGHT | BMI | Region | SYSTOLIC | BMI SMOKERS | BMI NONSMOKERS | BMI | HDL | |||||

68 | 0 | 90 | 95 | 113 | 45.2 | 151.6 | 19.7 | 4 | 132 | 28.1 | 19.7 | 19.7 | 95 | |||||

51 | 0 | 94 | 71 | 98 | 150.4 | 159.7 | 59.0 | 2 | 120 | 37.0 | 59.0 | 59.0 | 71 | |||||

18 | 0 | 68 | 62 | 97 | 71.5 | 158.4 | 28.5 | 2 | 120 | 36.5 | 28.5 | 28.5 | 62 | |||||

18 | 0 | 90 | 66 | 76 | 74.0 | 173.6 | 24.6 | 3 | 106 | 23.1 | 24.6 | 24.6 | 66 | |||||

20 | 0 | 82 | 78 | 140 | 64.0 | 160.1 | 25.0 | 2 | 110 | 20.2 | 25.0 | 25.0 | 78 | |||||

45 | 0 | 80 | 45 | 112 | 92.8 | 164.8 | 34.2 | 1 | 146 | 29.6 | 34.2 | 34.2 | 45 | |||||

51 | 0 | 74 | 47 | 112 | 85.9 | 172.1 | 29.0 | 4 | 128 | 24.9 | 29.0 | 29.0 | 47 | |||||

63 | 0 | 56 | 52 | 121 | 105.5 | 153.2 | 45.0 | 2 | 156 | 19.9 | 45.0 | 45.0 | 52 | |||||

80 | 0 | 100 | 65 | 120 | 43.3 | 134.5 | 23.9 | 1 | 122 | 25.8 | 23.9 | 23.9 | 65 | |||||

59 | 0 | 74 | 63 | 119 | 114.9 | 169.1 | 40.2 | 3 | 124 | 26.0 | 40.2 | 40.2 | 63 | |||||

33 | 0 | 76 | 45 | 111 | 89.1 | 160.2 | 34.7 | 1 | 108 | 33.7 | 34.7 | 34.7 | 45 | |||||

60 | 0 | 76 | 86 | 95 | 58.5 | 157.8 | 23.5 | 2 | 136 | 23.4 | 23.5 | 23.5 | 86 | |||||

38 | 0 | 86 | 49 | 85 | 57.2 | 166.3 | 20.7 | 4 | 112 | 32.7 | 20.7 | 20.7 | 49 | |||||

68 | 0 | 74 | 57 | 135 | 81.4 | 158.4 | 32.4 | 1 | 136 | 26.8 | 32.4 | 32.4 | 57 | |||||

21 | 0 | 66 | 63 | 146 | 95.6 | 177.8 | 30.2 | 3 | 112 | 18.1 | 30.2 | 30.2 | 63 | |||||

37 | 0 | 62 | 65 | 148 | 86.5 | 152.4 | 37.2 | 3 | 110 | 21.3 | 37.2 | 37.2 | 65 | |||||

69 | 0 | 78 | 47 | 96 | 79.1 | 164.1 | 29.4 | 3 | 142 | 23.9 | 29.4 | 29.4 | 47 | |||||

46 | 0 | 68 | 56 | 143 | 68.4 | 160.6 | 26.5 | 4 | 112 | 25.2 | 26.5 | 26.5 | 56 | |||||

41 | 0 | 62 | 46 | 75 | 85.7 | 167.7 | 30.5 | 4 | 102 | 22.8 | 30.5 | 30.5 | 46 | |||||

80 | 0 | 62 | 62 | 104 | 50.4 | 158.8 | 20.0 | 1 | 130 | 29.7 | 20.0 | 20.0 | 62 | |||||

41 | 0 | 74 | 61 | 180 | 72.1 | 156.5 | 29.4 | 2 | 98 | 31.2 | 29.4 | 29.4 | 61 | |||||

68 | 0 | 104 | 68 | 99 | 77.2 | 157.6 | 31.1 | 3 | 140 | 44.2 | 31.1 | 31.1 | 68 | |||||

42 | 0 | 54 | 66 | 76 | 83.3 | 169.7 | 28.9 | 2 | 126 | 29.3 | 28.9 | 28.9 | 66 | |||||

64 | 0 | 74 | 61 | 121 | 88.6 | 155.0 | 36.9 | 2 | 120 | 31.6 | 36.9 | 36.9 | 61 | |||||

33 | 0 | 74 | 40 | 85 | 84.6 | 170.6 | 29.1 | 1 | 114 | 35.0 | 29.1 | 29.1 | 40 | |||||

63 | 0 | 84 | 64 | 98 | 81.0 | 160.1 | 31.6 | 1 | 114 | 27.1 | 31.6 | 31.6 | 64 | |||||

60 | 0 | 60 | 81 | 99 | 53.5 | 156.4 | 21.9 | 1 | 186 | 29.6 | 21.9 | 21.9 | 81 | |||||

35 | 1 | 54 | 68 | 100 | 84.1 | 172.9 | 28.1 | 4 | 126 | 28.1 | 68 | |||||||

44 | 1 | 66 | 40 | 122 | 112.8 | 174.6 | 37.0 | 3 | 128 | 37.0 | 40 | |||||||

37 | 1 | 56 | 57 | 71 | 123.9 | 184.3 | 36.5 | 2 | 114 | 36.5 | 57 | |||||||

80 | 1 | 80 | 47 | 58 | 76.5 | 182.0 | 23.1 | 3 | 96 | 23.1 | 47 | |||||||

18 | 1 | 72 | 47 | 87 | 71.7 | 188.4 | 20.2 | 3 | 120 | 20.2 | 47 | |||||||

62 | 1 | 64 | 43 | 79 | 90.0 | 174.3 | 29.6 | 3 | 136 | 29.6 | 43 | |||||||

41 | 1 | 64 | 63 | 133 | 70.6 | 168.5 | 24.9 | 2 | 106 | 24.9 | 63 | |||||||

36 | 1 | 96 | 97 | 251 | 64.8 | 180.3 | 19.9 | 2 | 114 | 19.9 | 97 | |||||||

80 | 1 | 58 | 34 | 69 | 76.6 | 172.2 | 25.8 | 1 | 136 | 25.8 | 34 | |||||||

55 | 1 | 66 | 63 | 63 | 93.7 | 189.7 | 26.0 | 2 | 120 | 26.0 | 63 | |||||||

32 | 1 | 58 | 58 | 140 | 107.4 | 178.5 | 33.7 | 1 | 122 | 33.7 | 58 | |||||||

27 | 1 | 58 | 39 | 86 | 74.6 | 178.7 | 23.4 | 2 | 120 | 23.4 | 39 | |||||||

62 | 1 | 68 | 26 | 122 | 106.0 | 180.0 | 32.7 | 1 | 142 | 32.7 | 26 | |||||||

24 | 1 | 70 | 62 | 144 | 84.4 | 177.5 | 26.8 | 2 | 120 | 26.8 | 62 | |||||||

19 | 1 | 84 | 41 | 69 | 59.6 | 181.3 | 18.1 | 3 | 108 | 18.1 | 41 | |||||||

80 | 1 | 58 | 74 | 182 | 63.4 | 172.6 | 21.3 | 3 | 160 | 21.3 | 74 | |||||||

27 | 1 | 78 | 65 | 158 | 70.4 | 171.5 | 23.9 | 4 | 118 | 23.9 | 65 | |||||||

62 | 1 | 66 | 44 | 72 | 69.9 | 166.4 | 25.2 | 1 | 108 | 25.2 | 44 | |||||||

35 | 1 | 86 | 46 | 126 | 63.7 | 167.1 | 22.8 | 1 | 120 | 22.8 | 46 | |||||||

24 | 1 | 70 | 47 | 104 | 90.2 | 174.2 | 29.7 | 3 | 106 | 29.7 | 47 | |||||||

28 | 1 | 54 | 39 | 123 | 99.4 | 178.6 | 31.2 | 3 | 128 | 31.2 | 39 | |||||||

58 | 1 | 84 | 36 | 118 | 127.8 | 170.0 | 44.2 | 1 | 128 | 44.2 | 36 | |||||||

18 | 1 | 72 | 60 | 84 | 88.3 | 173.5 | 29.3 | 3 | 128 | 29.3 | 60 | |||||||

46 | 1 | 74 | 42 | 153 | 94.6 | 173.1 | 31.6 | 3 | 138 | 31.6 | 42 | |||||||

45 | 1 | 64 | 45 | 167 | 119.8 | 185.1 | 35.0 | 4 | 116 | 35.0 | 45 | |||||||

27 | 1 | 66 | 49 | 146 | 78.8 | 170.5 | 27.1 | 3 | 112 | 27.1 | 49 | |||||||

69 | 1 | 62 | 35 | 84 | 84.4 | 169.0 | 29.6 | 1 | 120 | 29.6 | 35 |

BMI – HDL RelationShip

HDL 19.7 59 28.5 24.6 25 34.200000000000003 29 45 23.9 40.200000000000003 34.700000000000003 23.5 20.7 32.4 30.2 37.200000000000003 29.4 26.5 30.5 20 29.4 31.1 28.9 36.9 29.1 31.6 21.9 28.1 37 36.5 23.1 20.2 29.6 24.9 19.899999999999999 25.8 26 33.700000000000003 23.4 32.700000000000003 26.8 18.100000000000001 21.3 23.9 25.2 22.8 29.7 31.2 44.2 29.3 31.6 35 27.1 29.6 95 71 62 66 78 45 47 52 65 63 45 86 49 57 63 65 47 56 46 62 61 68 66 61 40 64 81 68 40 57 47 47 43 63 97 34 63 58 39 26 62 41 74 65 44 46 47 39 36 60 42 45 49 35

BMI

HDL

## Sheet2

## Sheet3

****THIS DISCUSSION IS DIVIDE IN TWO PARTS –**

0.

**MAIN DISCUSSION POST BY WEDNESDAY 6/14/2023 BEFORE 8:00 PM EST **

0.

**TWO REPLIES BY FRIDAY 06/16/2023 BEFORE 8:00 PM EST**

**CORRELATION IN YOUR LIFE**

**Graphical Relationship**

· After you create a scatterplot (see below) for the data in the BMI and HDL cholesterol columns (from the data set ST3001Data_L_Rivera)

###
**Instructions: **

__**Use the data from ST3001Data_L_Rivera – see excel document attached**__

1. Using Excel, calculate the linear correlation coefficient between the data in the BMI and HDL cholesterol columns.

2. Explain the mathematical relationship between BMI and HDL cholesterol, based on the linear correlation coefficient. Be certain to include comments about the magnitude (strength) and the direction (positive or negative) of the correlation. As BMI increases, what happens to HDL cholesterol?

**Linear Regression and Prediction**

· Let’s say we wanted to predict the HDL cholesterol level of a patient based on their BMI.

1. Using this sample data, perform a linear regression to determine the line of best fit. Use BMI as your

*x* (independent) variable and HDL as your

*y* (response) variable. Use four (4) places after the decimal in your answer. Paste it in your report.

BMI – HDL RelationShip

HDL 19.7 59 28.5 24.6 25 34.200000000000003 29 45 23.9 40.200000000000003 34.700000000000003 23.5 20.7 32.4 30.2 37.200000000000003 29.4 26.5 30.5 20 29.4 31.1 28.9 36.9 29.1 31.6 21.9 28.1 37 36.5 23.1 20.2 29.6 24.9 19.899999999999999 25.8 26 33.700000000000003 23.4 32.700000000000003 26.8 18.100000000000001 21.3 23.9 25.2 22.8 29.7 31.2 44.2 29.3 31.6 35 27.1 29.6 95 71 62 66 78 45 47 52 65 63 45 86 49 57 63 65 47 56 46 62 61 68 66 61 40 64 81 68 40 57 47 47 43 63 97 34 63 58 39 26 62 41 74 65 44 46 47 39 36 60 42 45 49 35

BMI

HDL

**Response 1 – Instructions**

· State your peers R-squared (

*R2*) value, as well as the

*R2* value you computed between BMI and HDL cholesterol level.

· Explain which of the relationships is stronger, your peers or yours? Use the

*R2* value to justify your reasoning.

· Calculate the coefficient of determination (

*R2* value) for your peer’s data. Explain what this indicates about the relationship between BMI and HDL cholesterol.

· Explain one reason we cannot assume that changes in HDL cholesterol are caused by changes in BMI.

**WEEK 3 – Discussion _ **

**Mariah Vickerman**

The linear correlation coefficient between BMI and HDL in my data set was -0.29796. The relationship between BMI and HDL cholesterol is a weak negative correlation. I concluded that it is weak because the correlation coefficient is closer to 0 than 1 or -1. This also means that as BMI Increases, HDL cholesterol would decrease because they have a negative correlation. Lastly, the line of best fit is y= -0.9248x+81.8917.

HDL vs BMI for smokers and non-smokers

BMI

y = -0.096x + 33.871

52 65 63 45 86 49 57 63 65 47 56 46 62 61 68 66 61 40 64 81 53 39 82 62 84 55 138 54 57 41 57 47 47 43 63 97 34 63 58 39 26 62 41 74 65 44 46 47 39 36 60 42 45 49 35 46 31 46 67 49 40 42 54 45 23.9 40.200000000000003 34.700000000000003 23.5 20.7 32.4 30.2 37.200000000000003 29.4 26.5 30.5 20 29.4 31.1 28.9 36.9 29.1 31.6 21.9 34.6 27.5 21.6 25.8 25.7 26.2 21.5 29.4 34.6 24.4 36.5 23.1 20.2 29.6 24.9 19.899999999999999 25.8 26 33.700000000000003 23.4 32.700000000000003 26.8 18.100000000000001 21.3 23.9 25.2 22.8 29.7 31.2 44.2 29.3 31.6 35 27.1 29.6 26.8 29.2 27.6 26.2 30.7 33.9 31.5 26.4

HDL

BMI

**Response 2 – Instructions**

· Use the regression equation that your peer created to model the relationship between BMI and HDL cholesterol.

· What would you predict the HDL would be for a patient with a BMI of 25? Show your calculations.

· What would you predict the HDL would be for a patient with a BMI of 40? Show your calculations.

· What did you predict would happen to HDL cholesterol as the BMI increased in your main post? Did these predictions support your prediction? Why, or why not?

## Week 3 _ Discussion _

Arian Aman Pakray

**Graphical Relationship**

· Using Excel, calculate the linear correlation coefficient between the data in the BMI and HDL cholesterol columns.

Linear correlation coefficient is -0.331434003

· Explain the mathematical relationship between BMI and HDL cholesterol, based on the linear correlation coefficient. Be certain to include comments about the magnitude (strength) and the direction (positive or negative) of the correlation. As BMI increases, what happens to HDL cholesterol?

The mathematical relationship between BMI and HDL is a weak negative correlation. Correlations are numbers between -1 and 1. The closer it is to either -1 or 1 means a stronger magnitude the closer to 0 means a weaker magnitude. Since the value is -0.33, it is closer to 0 than -1, so it’s a weak negative correlation. Therefore, as BMI increases, HDL cholesterol decreases.

**Linear Regression and Prediction**

· Let’s say we wanted to predict the HDL cholesterol level of a patient based on their BMI.

· Using this sample data, perform a linear regression to determine the line of best fit. Use BMI as your

*x* (independent) variable and HDL as your

*y* (response) variable. Use four (4) places after the decimal in your answer. Paste it in your report.

· What is the equation of the line of best fit (linear regression equation)? Present your answer in form.

y= -1.0104x + 83.7387

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