P$6-68$A$.$ Analyze cost behavior at a hospital using various cost estimation methods $($Learning Objectives $1,2,3,4,$ & $5)$

Sandy Dawson is the Chief Operating Officer at Mercy Hospital in Atlanta, Georgia. She is analyzing the hospital$$s overhead costs but is not sure whether nursing hours or the number of patient days would be the best cost driver to use for predicting the hospital$$s overhead. She has gathered the following information for the last six months of the most recent year:

The table shows the following data with the cost in dollars:

July Hospital Overhead costs: $483,000$ Nursing hours: $24,500$ Number or patient days: $3,790$ Overhead cost per Nursing hour: $19\mathrm{.}71$ Overhead cost per patient Day: $127\mathrm{.}44$

August Hospital Overhead costs: $535,000$ Nursing hours: $28,500$ Number or patient days: $4,310$ Overhead cost per Nursing hour: $18\mathrm{.}77$ Overhead cost per patient Day: $124\mathrm{.}13$

September Hospital Overhead costs: $411,000$ Nursing hours: $19,500$ Number or patient days: $4,230$ Overhead cost per Nursing hour: $21\mathrm{.}08$ Overhead cost per patient Day: $97\mathrm{.}16$

October Hospital Overhead costs: $451,000$ Nursing hours: $20,500$ Number or patient days: $3,450$ Overhead cost per Nursing hour: $22\mathrm{.}00$ Overhead cost per patient Day: $130\mathrm{.}72$

November Hospital Overhead costs: $576,000$ Nursing hours: $32,000$ Number or patient days: $5,710$ Overhead cost per Nursing hour: $18\mathrm{.}00$ Overhead cost per patient Day: $100\mathrm{.}88$

December Hospital Overhead costs: $446,000$ Nursing hours: $20,000$ Number or patient days: $3,290$

Requirements $1.$ Are the hospital$$s overhead costs fixed, variable, or mixed? Explain$\mathrm{.}2.$ Graph the hospital$$s overhead costs against nursing hours. Use Excel or graph by hand.

$3.$ Graph the hospital$$s overhead costs against the number of patient days. Use Excel or graph by hand.

$4.$ Do the data appear to be sound, or do you see any potential data problems? Explain.

$5.$ Use the high$-$low method to determine the hospital$$s cost equation using nursing hours as the cost driver. Predict total overhead costs if $25,500$ nursing hours are predicted for the month.

$6.$ Dawson runs a regression analysis using nursing hours as the cost driver to predict total hospital overhead costs. The Excel output from the regression analysis is as follows:

The information is as follows: Summary output $$ nursing hours as cost driver Regression Statistics Multiple R is $0\mathrm{.}984685$ R Square is $0\mathrm{.}969605$ Adjusted R Square is $0\mathrm{.}962006$ Standard Error is $11,992\mathrm{.}70481$ Observations is $6$ ANOVA Regression: df: $1$; SS: $18,352,033,459$; MS: $18,352,033,459$; F: $127\mathrm{.}599774$; Significance F: $0\mathrm{.}00035$ Residual: df: $4$; SS: $525,299,875$; MS: $143,824,969$; F: NA; Significance F: NA Total: df: $5$; SS: $18,877,333,334$; MS: NA; F: NA; Significance F: NA Intercept: Coefficients: $199,609\mathrm{.}79$; Standard Error: $25,618\mathrm{.}85$; t Stat: $7\mathrm{.}792$; P$-$value: $0\mathrm{.}001$; Lower $95\%$: $128,480\mathrm{.}456$; Upper $95\%$: $270,739\mathrm{.}118.$ X Variable $1$: Coefficients: $11\mathrm{.}75$; Standard Error: $1\mathrm{.}041$; t Stat: $11\mathrm{.}296$; P$-$value: $0\mathrm{.}000$; Lower $95\%$: $8\mathrm{.}865$; Upper $95\%$: $14\mathrm{.}643.432$

If $25,500$ nursing hours are predicted for the month, what is the total predicted hospital overhead?

$7.$ Dawson then ran the regression analysis using number of patient days as the cost driver. The Excel output from the regression is shown here: The information is as follows: Summary output, using number of patient days as cost driver. Regression statistics Multiple R is $0\mathrm{.}750775$ R Square is $0\mathrm{.}563662$ Adjusted R Square is $0\mathrm{.}454578$ Standard Error is $45,438\mathrm{.}70968$ Observations is $6$ ANOVA Regression: df: $1$; SS: $10,668,627,982$; MS: $10,668,627,982$; F: $5\mathrm{.}167216$; Significance F: $0\mathrm{.}08543$ Residual: df: $4$; SS: $8,258,705,351$; MS: $2,064,676,338$; F: NA; Significance F: NA Total: df: $5$; SS: $18,927,333,333$; MS: NA; F: NA; Significance F: NA Intercept: Coefficients: $265,475\mathrm{.}95$; Standard Error: $97,762\mathrm{.}101$; t Stat: $2\mathrm{.}176$; P$-$value: $0\mathrm{.}053$; lower $95\%$: negative $5,955\mathrm{.}158$; Upper $95\%$: $536,907\mathrm{.}056$ X Variable $1$: Coefficients: $52\mathrm{.}83$; Standard Error: $23\mathrm{.}241$; t Stat: $2\mathrm{.}273$; P$-$value: $0\mathrm{.}085$; lower $95\%$: negative $11\mathrm{.}697$; Upper $95\%$: $117\mathrm{.}359$

If $3,680$ patient days are predicted for the month, what is the total predicted hospital overhead?

$8.$ Which regression analysis $($using nursing hours or using number of patient days as the cost driver$)$ produces the best cost equation? Explain your answer.