Answer:
Average Rate of Pay = $ 5.23 /hr
Step-by-step 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:
<u>y = -13.83 + 5.23x</u>
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)
<u>Average Rate of Pay = $ 5.23 /hr</u>