$****************************$PLEASE ANSWER NEATLY AND CORRECTLY USING R$-$STUDIO AND PROVIDE CODE.$*******************************************$PLEASE ANSWER NEATLY AND CORRECTLY USING R$-$STUDIO AND PROVIDE CODE.$*******************************************$PLEASE ANSWER NEATLY AND CORRECTLY USING R$-$STUDIO AND PROVIDE CODE.$*******************************************$PLEASE ANSWER NEATLY AND CORRECTLY USING R$-$STUDIO AND PROVIDE CODE.$***************0$ Earnings of Mexican street vendors. Refer to the World Development $($February $1998)$ study of street vendors' earnings $($y$),$ Exercise $4\mathrm{.}6($p$.184).$ The SAS printout below shows both a $95\%$ prediction interval for y and a $95\%$ confidence interval for E$($y$)$ for a $45-$year$-$old vendor who works $10$ hours a day $($i$.$e$.,$ for x$\_1=45$ and $.$x$\_2=10).($a$)$ Interpret the $95\%$ prediction interval for y in the words of the problem. $($b$)$ Interpret the $95\%$ confidence interval for E$($y$)$ in the words of the problem.$($c$)$ Note that the interval of part a is wider than the interval of part b$.$ Will this always be true? Explain.STREETVEN Source: Adapted from Smith, P$.$ A$.,$ and Metzger, M$.$ R$.$ "The return to education: Street vendors in Mexico," World Development, Vol. $26,$ No$.2,$ Feb. $1998,$ pp$.289-296.$