Suppose You Are Interested in Explaining the Effect That Family

Suppose you are interested in explaining the effect that family income (thousands)has on child birth weight and you are concerned that the true marginal effects differ for at different points in the birth weight distribution.In a sample of 22,365 live births,you estimate following $\begin{array}{llll}10^{\text {th }} \text { Percentile:} & Burt \widehat {h W }etght _ { i } =&5.583+0.086 \text { Income }_{i}&+0.084 \text { Education }_{i} \\&& (1.473)(0.032)&( (0.029)\\25^{\text {th }}\text { Percentile:} & Burt \widehat {h W }etght _ { i } =& 6.012+0.073 \text { Income }_{i}&+0.076 \text { Education }_{i}\\&& (2.533) (0.027)& (0.038) \\50^{\text {th }} \text { Percentile:} & Burt \widehat {h W }etght _ { i } =& 6.309+0.069 \text { Income }_{i}&+0.091 \text { Education }_{i}\\&& (1.925)(0.022)&(0.042) \\75^{\text {th }} \text { Percentile:} & Burt \widehat {h W }etght _ { i } =& 6.733+0.057 \text { income }_{i}&+0.074 \text { Education }_{i}\\&& (2.437)(0.026)& (0.029) \\90^{\text {th }} \text { Percentile:} & Burt \widehat {h W }etght _ { i } =& 7.024+0.033 \text { Income }_{i}&+0.065 \text { Education }_{i}\\&& (1.847)(0.013) & (0.031) \\\end{array}$

a)What is quantile regression? Which variable is the quantile of?
b)In what circumstances would quantile regression be preferable to OLS?
c)Discuss the results presented above.