# Question on predicting values from linear regression

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

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

Is this correct?