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QUESTION $1.[40$ points$]$ The nurse manager of an intensive care unit would like to develop a budget for medical supplies that is based on patient days provided in Table I. Period Patient Days Cost $132546,718232353,200332647,376425331,240527841,561625635,108724433,510817628,830916729,5681024532,3541128138,7781229442,6301325535,8761426530,5301526728,3251623529,9871718323,5481815622,454$ Table I $1.$a$.$ Using a linear regression model, develop predictions for costs in periods $1$ through $18$ based on patient days. $1.$b$.$ What is the prediction error in period $1?$ What is the prediction error in period $18?1.$c$.$ Predict costs when patient days are $200,220,$ and $280.$ OUESTION $1.[40$ points$]$ The nurse manager of an intensive care unit would like to develop a budget for medical supplies that is based on patient days provided in Table I.

$\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|\}$

$\backslash$hline Period & Patient Days & Cost $\backslash \backslash$

$\backslash$hline $1$ & $325$ & $46,718\backslash \backslash$

$\backslash$hline $2$ & $323$ & $53,200\backslash \backslash$

$\backslash$hline $3$ & $326$ & $47,376\backslash \backslash$

$\backslash$hline $4$ & $253$ & $31,240\backslash \backslash$

$\backslash$hline $5$ & $278$ & $41,561\backslash \backslash$

$\backslash$hline $6$ & $256$ & $35,108\backslash \backslash$

$\backslash$hline $7$ & $244$ & $33,510\backslash \backslash$

$\backslash$hline $8$ & $176$ & $28,830\backslash \backslash$

$\backslash$hline $9$ & $167$ & $29,568\backslash \backslash$

$\backslash$hline $10$ & $245$ & $32,354\backslash \backslash$

$\backslash$hline $11$ & $281$ & $38,778\backslash \backslash$

$\backslash$hline $12$ & $294$ & $42,630\backslash \backslash$

$\backslash$hline $13$ & $255$ & $35,876\backslash \backslash$

$\backslash$hline $14$ & $265$ & $30,530\backslash \backslash$

$\backslash$hline $15$ & $267$ & $28,325\backslash \backslash$

$\backslash$hline $16$ & $235$ & $29,987\backslash \backslash$

$\backslash$hline $17$ & $183$ & $23,548\backslash \backslash$

$\backslash$hline $18$ & $156$ & $22,454\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$

Table I

$1.$a$.$ Using a linear regression model, develop predictions for costs in periods $1$ through $18$ based on patient days.

$1.$b$.$ What is the prediction error in period $1?$ What is the prediction error in period $18?$

$1.$c$.$ Predict costs when patient days are $200,220,$ and $280.$