John’s parents recorded his height at various ages between 36 and 66 months.
Below is a record of the results:
Age(A, months) 36 48 54 60 66
Height(H, inches) 34 38 41 43 45

(a) Determine the equation of the least-squares regression line of John’s height on age.

(b) John’s parents decide to use the least-squares regression line of John’s height on age to predict his height at age 21 years (252 months). What conclusion can we draw?

Step-by-step explanation:

a)General least square regression line is ,

Where,a=intercept. b= slope

To get line just find values of a and b.

Use Excel to find values.

First enter values of variable "age" that is y in the column A that is A1to A5 and values of variable "height" in the column B, B1 to B5.

Then for value of a use functufuas ,

=INTERCEPT(A1:A5,B1:B5)

Then hit enter ,therefore a=20.4595

For b use function as. =SLOPE(A1:A5,B1:B5)

Then hit enter.therefore b=0.3738

Therefore equation of least square regression line is

Y=20.4595+(0.3738*x)

b) to predict height at age 21 years or 252 month just put value of x=252 in the above equation.

Y=20.4595+(0.3738+252)

Y=20.4595+94.1976

Y=114.6571

Conclusion: height will be 114.6571 inches when age change by 1 unit.