Question

There are five families that each have one child. Each of them hires Riley as a babysitter. Because the children she babysits are different ages, Riley charges each family a different amount. To visualize her earnings, Riley recorded and plotted her pay from each job. Using the scatterplot, calculate her average rate of pay.

Answer 1

Average Rate of Pay = $ 5.23 /hr

Explanation:

We have a data in form of Hours of Baby Sitting and Amount of Pay. Since the Amount of pay depends upon the Hours of Baby Sitting. Thus, we take y = Amount of Pay, while x = Hours of Baby Sitting. So, the data becomes:

x (Hours) = 12 13 16 17 20

y ($) = 54 56 65 64 100

The statistical data calculated is:

∑x = 78, ∑x² = 1258, ∑y = 339, ∑xy = 5504, n = no. of data points = 5

Now, we use linear regression model to fit a straight line to this data.

y = a + bx --------- eqn (1)

where,

b = [ n∑xy - ∑x.∑y]/[n∑x² -(∑x)²]

b = [ (5)(5504) - (78)(339)]/[(5)(1258) - (78)²]

b = 5.23

and,

a = (∑xy - b∑x²)/∑x

a = [5504 - (5.23)(1258)]/78

a = -13.83

Therefore, eqn (1) becomes:

y = -13.83 + 5.23x

The graph plot of this straight line fit is provided in the attachments.

Now, we derivate the equation with respect to x, to get the average rate of pay:

Average Rate of Pay = dy/dx = d/dx(-13.83 + 5.23x)

Average Rate of Pay = $ 5.23 /hr