Question on predicting values from linear regression

Question

I have this set of values and Table 1 shows the average driving distance (in yards) for players on the men's (PGA) and women's (LPGA) professional golf tours from 1992 through 2003.

I need to answer the following questions:

(i) Estimate the average driving distances for both tours in the year 2011.

(ii) When will the average driving distance for the men's tour be 310 yards?

(iii) When will the average driving distance for the women's tour be 270 yards?

(iv) Will the average driving distance for the women's tour ever be higher than the average for the men's tour? If so, when?

For PGA Driving Distance, my regression equation is:

$\hat{y}=-4186.568298+ 2.231118881x$

For LPGA Driving Distance, my regression equation is:

$\hat{y}=-4367.171212+ 2.304545455x$

(i) I have: PGA - 300.2 yards, LPGA - 267.3 yards

(ii) I solved the equation: $310 = -4186.568298+ 2.231118881x$

and got $2015.4$ so the answer would be 2015.

(iii) I solved the equation: $270= -4367.171212+2.304545455x$

and got $2012.19$ so the answer would be 2012.

(iv) I solved: -4186.568298+ 2.231118881x < -4367.171212+2.304545455x$ and got

$180.602914 < 0.073426574x$

$2459.6396667<x$

So after the year 2459.6396667 the average driving distance for women will be higher than men.

Is this correct?

Answer 1

Your regression equations are correct. Regarding the answers, given the wording of the questions, the answers are correct.

However, given that these average distances are published once a year, it would have been better had the questions been slightly different. For instance, (ii) should have been: "(ii) When will the average driving distance for the men's tour be 310 yards or more?". Then, the years in asnwers should be rounded up: 2015.4 would have to be rounded up to 2016. Why? The average driving distance in PGA in year 2015 would be 309.1 and that in 2016 would be 311.4. So in year 2016, the average driving distance would have crossed 310 yards. Similarly, other two answers should be 2013 and 2460.

PS: If you want to check answers in linear aggression, you could use this feature of Excel.