For married couples with one or more offspring, a demographic study was conducted to determine the effect of the husband's annual income (at marriage) on the time (in months) between marriage and the birth of the first child. The following table gives the husband's annual income (INC) and the time between marriage and the birth of the first child (TIME) for a hypothetical sample of 20 couples.

a. On the scatter diagram above, sketch by eye a line that fits the data reasonably well. Comment on the relationship between TIME (Y) and INC (X).
b. Determine the least-squares estimates of the slope (β1) and intercept (β0) for the straight-line regression of TIME (F) on INC (X).
c. Draw the estimated regression line on the accompanying scatter diagram. Comment on how well this line fits the data.
d. Are any of the assumptions for straight-line regression clearly not satisfied in this example?
e. Test the null hypothesis that the true slope is 0. Interpret the results of this test.
f. Can you suggest a model that would describe the TIME-INC relationship better than a straight line does?

INC TIME INC TIME 5,775 16.20 9,800 35.00 13.795 37.20 4,120 25,01524.40 12,200 36.75 7400 31.75 9.340 30.00 20,170 36.00 22.400 30.80 9.70 24,210 20.00 9,625 38.20 18.000 44.0 4,608 41.25 3,00044.00 9.20 20.00 40.20 18180 3200 15,385 39.20 9,00 5,400 6,440 9,000 50 40 a 20 10 10 15 INC ( 00s 20 25 30