Question

1. Calculate the Correlation between height and weight, using centimeters and kilograms

2. Calculate the Correlation between height and weight, using inches and pounds

3. Compare these correlations. What would you conclude?

4. Create a Scatter plot graph of these data.

Graph:

• Select Pounds in the X axis and Inches in the Y
• Insert a scatter graph
• Click on the first graph
• Click on Drawing Tools and then layout: Select Axis Titles: write the titles
• Do the same thing for the title, but select chart title
• Click on Format and then layout: Select Trend line and Linear Trend line.
• Click on Format again and then layout: Select Trend line

Click on more options and check the box that says R2 and Equation.

cm	kg		pounds	inches
175.3	86.6		191	69
172.7	72.6		160	68
177.8	71.2		157	70
182.9	86.6		191	72
165.1	63.9		141	65
175.3	83.9		185	69
182.9	95.2		210	72
165.1	67.6		149	65
177.8	76.6		169	70
172.7	78.5		173	68
172.7	68.0		150	68
175.3	65.3		144	69
152.4	66.2		146	60

	155.7	70.3		155	61.3
	163.8	83.0		183	64.5
Mean
SD
inches vs. Pounds r
cms vs. kg r

Answer 1

cm	kg		pounds	inches
175.3	86.6		191	69
172.7	72.6		160	68
177.8	71.2		157	70
182.9	86.6		191	72
165.1	63.9		141	65
175.3	83.9		185	69
182.9	95.2		210	72
165.1	67.6		149	65
177.8	76.6		169	70
172.7	78.5		173	68
172.7	68		150	68
175.3	65.3		144	69
152.4	66.2		146	60
155.7	70.3		155	61.3
163.8	83		183	64.5

1) X (cm) Values
∑X = 2567.5
Mean = 171.167
∑(X - M_x)² = SS_x = 1140.933

Y(kg) Values
∑ = 1135.5
Mean = 75.7
∑(Y - M_y)² = SS_y = 1268.62

X and Y Combined
N = 15
∑(X - M_x)(Y - M_y) = 685.26

R Calculation
r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

r = 685.26 / √((1140.933)(1268.62)) = 0.5696

2 )X(pounds) Values
∑ X= 2504
Mean = 166.933
∑(X - M_x)² = SS_x = 6172.933

Y (inches) Values
∑Y = 1010.8
Mean = 67.387
∑(Y - M_y)² = SS_y = 176.497

X and Y Combined
N = 15
∑(X - M_x)(Y - M_y) = 594.787

R Calculation
r = ∑((X - M_y)(Y - M_x)) / √((SS_x)(SS_y))

r = 594.787 / √((6172.933)(176.497)) = 0.5698

3) since the correlation between the weights and heights in both the measurements are same so there is no effect of changing the measurements of data om correlation , it will remain same.

4)