Question

The director of surgery at a local hospital is interested in understanding his unit’s costs. An assistant collected data for the past 36 months on unit cost (labor, supplies, and so on) along with the number of procedures performed in the unit. The assistant analyzed the data using a spreadsheet program, and the following output was generated: Equation Intercept $ 1,018,000 Coefficient on procedures $ 235 Statistical data Correlation coefficient 0.578 R2 0.328 The unit is planning to perform an average 16,000 procedures per month for the coming year.

Required: a. Use the regression output to write the surgical unit cost equation.

b. Based on the cost equation, compute the estimated costs for the surgical unit per month for the coming year.

c. The director of surgery has asked you for advice on whether he should rely on the estimate. Yes No

Answer 1

a	The surgical unit cost equation using regression output for the hospital is as under:
	Here the Y dependent variable is the number of procedures per month.The estimated fixed cost
	of the hospital is $1018000.The independent variable of the hospital is number of procedures
	The total cost of the hospital is the sum of the fixed cost and variable cost
	The surgical cost equation using the regression output is as under:
	Total Cost	=	Intercept + variable cost*no of procedures
		=	$1018000+$235*No of procedures
b	The estimated number of procedures per month in the coming year was 16000
	Therefore the estimated cost for surgical unit per month in coming yr would be as under:
	Total Cost	=	Intercept+(variable cost * no of procedures)
		=	$1018000 +($235 *no of procedures)
		=	$1018000+($235*16000)
		=	$4,778,000
c	The regression statistical data shows that the coefficient of determination R^2 is .328 which is
	32.8% .The R^2 is interpreted as the proportion of variation in Y explained by right hand side of
	regression equation R^2 of .328 means that 32.8% of the variability of the dependent variables
	about the mean is explained by the variability of the independent variables about its mean.
	The higher the R^2 the better the regression line fits the data.if R^2 is closer to zero then it means
	the data points are poorer fit to the regression line.The poorer fit to regression line means the
	equation of cost estimation and behavior pattern is not reliable.