Question

8. For people in Anchorage working at a part time job, there is approximately a linear relationship between “hourly wage” and “age”. The relationship

can be represented by: Y’ = 0.25(x) + 3.2, where Y represents hourly wage

(in dollars) and X represents age (in years). Joseph is 25 years old and his hourly wage is 10.00. What is the prediction error for Joseph’s wage?

1. -.55
2. +.55
3. 10.00
4. 9.45

b) In the above equation, explain what 0.25X means.

c) In the above equation explain what +3.2 means.

Answer 1

Here equation is given as  Y’ = 0.25(x) + 3.2

Now for x=25,  Y’ = 0.25(25) + 3.2=9.45

Now Y is given as 10

So Prediction error for Joseph's wage is Y-Y’=10-9.45=+0.55

Hence answer here is B.+0.55

Let us first understand regression equation, y=slope*x+intercept

b. For Y’ = 0.25(x) + 3.2, here 0.25 is the slope value

As slope is positive, hence there is positive correlation between age and hours

Value 0.25 means, that for every increase in x, there is corresponding increase in y by 0.25 value

c. Now 3.2 is the intercept value, which is value of y when all x=0