Sarah’s parents are concerned that she seems short for her age. Their doctor has the following record of Sarah’s height:
Age: 36,48,51,54,57,60
Height: 82,93,94,98,99,103

Answer:

a) Please find the attached scatter plot

b) Y = 0.85·X + 51.843

c) The intercept = Sarah's height at birth

The slope = Sarah's monthly growth rate

d) Sarah's height in 50 years (600 months) will be 221.198 inches

d) The generality of the population stop growing taller when they reach 216 months old

Step-by-step explanation:

a) Please find attached the scatter plot included here

b) From Microsoft Excel, we have;

N = 6

(ΣX)² = 93636

ΣX = 306

ΣY = 569

ΣXY = 29325

ΣX² = 15966

The equation for the least squares regression line is Y = b·X + a

Where;

[tex]a = \dfrac{\sum Y - b\sum X}{N}[/tex]

[tex]b = \dfrac{N\sum XY - \left (\sum X \right )\left (\sum Y \right )}{N\sum X^{2} - \left (\sum X \right )^{2}}[/tex]

Substituting the values, gives;

[tex]b = \dfrac{6 \times 29325- 306 \times 569}{6 \times 15966 - 93636} = 0.85[/tex]

[tex]a = \dfrac{569 - 0.85 \times 306}{6} = 51.48\bar 3[/tex]

The equation of the least squares regression line is Y = 0.85·X + 51.843

c) The intercept gives the Sarah's height at birth, while the slope gives the increase in Sarah's height every month

d) In 50 years, which is equivalent to 600 months, we will have;

Y = 0.85 × 600 + 51.843 = 561.843 cm

2.54 cm = 1 inches

Therefore;

561.843 cm = 561.843 cm/2.41 × inches/cm ≈ 221.198 inches (18.43317 feet)

Sarah's height in 50 years (600 months) = 221.198 inches

d) The reason for the impossibly large height is that the generality of the population stop growing taller by 18 years of age which is 216 months.

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