c$.$ Compute and report the regression equation that predicts "amount of bill" with "number of diners." $($Negative amounts should be

indicated by a minus sign. Round "amount of bill" to $3$ decimal places and "number of diners" to $4$ decimal places.$)$

Amount of Bill $=$

$($Number of Diners$)$

d$-1.$ Report the regression equation that predicts "amount of tip" with "amount of bill." $($Negative amounts should be indicated by a

minus sign. Round your answers to $4$ decimal places.$)$

Amount of Tip $=$

$($Amount of Bill$).$

d$-2.$ Report the coefficient of determination. $($Round your answer to $2$ decimal places.$)$

Coefficient of determination

d$-3.$ Interpret the regression coefficient. $($Round your answer to $4$ decimal places.$)$

Regression coefficient e$.$ Predict the tip based on a bill amount of $$100.($Round your answer to $3$ decimal places.$)$

Predicted Amount of tipThe Conch Caf$,$ located in Gulf Shores, Alabama, features casual lunches with a great view of the Gulf of Mexico. To accommodate the increase in business during the summer vacation season, Fuzzy Conch, the owner, hires a large number of servers as seasonal help. When he interviews a prospective server, he would like to provide data on the amount a server can earn in tips. He believes that the amount of the bill and the number of diners are both related to the amount of the tip. He gathered the following sample information.

$\backslash$table$[[$Customer$,\backslash$table$[[$Amount of$],[$Tip$]],\backslash$table$[[$Amount of$],[$Bill$]],\backslash$table$[[$Number of$],[$Diners$]],$Customer,Amount of Tip,$\backslash$table$[[$Amount of$],[$Bill$]],\backslash$table$[[$Number of$],[$Diners$]]],[1,$$$7\mathrm{.}00,$$$48\mathrm{.}90,3,16,$$$3\mathrm{.}30,$$$23\mathrm{.}52,2],[2,3\mathrm{.}80,28\mathrm{.}30,2,17,3\mathrm{.}50,22\mathrm{.}30,2],[3,1\mathrm{.}00,10\mathrm{.}72,3,18,3\mathrm{.}18,32\mathrm{.}00,2],[4,3\mathrm{.}80,19\mathrm{.}89,3,19,5\mathrm{.}40,50\mathrm{.}09,4],[5,5\mathrm{.}00,28\mathrm{.}69,3,20,2\mathrm{.}18,17\mathrm{.}60,3],[6,4\mathrm{.}18,24\mathrm{.}90,2,21,5\mathrm{.}50,44\mathrm{.}40,4],[7,\mathrm{.}50,6\mathrm{.}31,1,22,3\mathrm{.}00,20\mathrm{.}34,2],[8,6\mathrm{.}00,49\mathrm{.}20,4,23,1\mathrm{.}18,19\mathrm{.}46,2],[9,5\mathrm{.}00,43\mathrm{.}33,3,24,3\mathrm{.}18,27\mathrm{.}10,3],[10,4\mathrm{.}68,31\mathrm{.}29,4,25,3\mathrm{.}00,21\mathrm{.}21,2],[11,5\mathrm{.}18,32\mathrm{.}94,4,26,6\mathrm{.}46,43\mathrm{.}45,4],[12,6\mathrm{.}00,34\mathrm{.}92,3,27,5\mathrm{.}60,28\mathrm{.}05,4],[13,4\mathrm{.}00,33\mathrm{.}98,4,28,2\mathrm{.}50,26\mathrm{.}32,2],[14,3\mathrm{.}28,22\mathrm{.}99,2,29,9\mathrm{.}18,56\mathrm{.}74,2],[15,0\mathrm{.}89,4\mathrm{.}72,1,30,8\mathrm{.}18,50\mathrm{.}72,5]]$

picture Click here for the Excel Data File

a$-1.$ Compute the following correlation matrix. $($Round your answers to $4$ decimal places.$)$

$\backslash$table$[[,$Correlation Matrix,,$],[,$Amount of Tip $($$$),$Amount of Bill $($$$),$Diners$],[$Amount of Tip $($$$),1,,],[$Amount of Bill $($$$),(0\mathrm{.}1319),,],[$Diners$,,,1]]$