Scatter Plot (x – Arm Span (inches) and y – Height(inches))
Predicted line of best fit: Heightinches=0.9557*Arm spaninches-1.6226y=0.9557x-1.6226Part Three:
On the x-axis (Arm Span) and on the y-axis (Height), in order to predict the person’s Height (inches) using their Arm Span (inches).
Equation (line of best Fit) : ŷ=0.9557x-1.6226x – x̄ y – ȳ (x – x̄)2 (y – ȳ)2 (x – x̄)(y – ȳ)
14
1
9
-21
-7
-1
3
-11
-6
4
15 13.8182
4.8182
6.8182
-25.1818
-7.1818
-0.1818
2.8182
-8.1818
-3.1818
1.8182
13.8182 196
1
81
441
49
1
9
121
36
16
225 196
1
81
441
49
1
9
121
36
16
225 193.4545
4.8182
61.3636
528.8182
50.2727
0.1818
8.4545
90
19.0909
7.2727 207.2727
0 0 1176 (SSx) 1225.6364 (SSy) 1171 (SPxy)
Sum of X = 506
Sum of Y = 486
Mean X = 46
Mean Y = 44.1818
Sum of squares (SSX) = 1176
Sum of products (SP) = 1171
Regression Equation = ŷ = mx + b
m = SPXY/SSx = 1171/1176 = 0.9957
b = MY – m*MX = 44.18 – (1*46) = -1.6226
ŷ = 0.9957X – 1.6226
Slope – It means that on average, an increase of 1 inch in Arm Span is associated with a decrease of 1.6226 inches in Height.
Y – Intercept – It means that on average, the expected Height is (b = -1.6226 inches)when a person’s Arm span is 0 inches. In this context it is impossible for a person to have an arm span of 0 inches.
Residuals:
X = 25 inches
y = 19 inches ŷ=0.9957 25- 1.6226≈23.27 inches
Residualx = 25 = 19 – 23.27 = -4.27 inchesX = 50 inches
y = 46 inches ŷ=0.9957 50- 1.6226≈48.16 inches
Residualx=50 = 46 – 48.16 =-2.16 inchesThere is a strong Positive linear correlation between a person’s Height and their Arm Span. A person’s Height increases as their Arm Span increases.
For a person whose Arm span = 66 inches:
x = 66 inches ŷ=0.9957 66- 1.6226≈64.09 inchesFor a person who is 74-inches tall:
ŷ=0.9957x- 1.6226= 74
0.9957x=74+1.62260.9957x=75.6226 x = 75.95 inches
