Month Number of Patient$-$ Days $($X$)$ Maintenance Cost $($Y$)$

January $5,600$ $$7,900$

February $7,100$ $$8,500$

March $5,000$ $$7,400$

April $6,500$ $$8,200$

May $7,300$ $$9,100$

June $8,000$ $$9,800$

July $6,200$ $$7,800$

Required:

$1.$ Find the cost formula using the high$-$low method

Step $1$: Find b per unit: Select high and low points: Change in Cost $($Y$)/$ Change in Activity $($X$)$

Step $2$: Find a $($fixed cost$)$: Using either high or low data point Y $=$ a$+($b $*$ X$).$

Find the Cost formula: Y$=$ a$+($b $*$ X$)$ and summarize below.

$2.$ Prepare scatterplot graph:

Highlight date in the table $($C$6$:D$12)$

In Cell G$4$ use the Insert tab, select Charts and select "Scatter"

Choice the chart with no lines connection the data points.

$3.$ Perform regression analysis:

Does data appear to be linear? If yes, proceed

Right click on any data point

Select "Add Trendline"

Under "Trendline Option" select "Linear"

Under "Trendline Name" select "Automatic"

Next to the word "Backward enter the value $(5,000)$ of lowest independent variable $($patient$-$days$)$

Check two boxes "Display Equation on chart" and "Display R$-$squared value on chart" and possibly other statisical measures.

$4.$ Summarize cost equation for each method.

High$-$low Method Regression Analysis

b $=($variable cost per unit$)$

a$=($fixed cost per mont$)$

Express the cost formula for each: Y$=$a $+$b$($x$)$

$5.$ Analysis:

$5$a$.$ Based on the regression analysis how do we know if high correlation exists? Explain.

$5$b$.$ Explain the t$-$value

$5$c$.$ Explain the standard error of the estimate $($SE$).$

$5$d$.$ Explain the p$-$value.

$5$e$.$ Predict the maintenance cost for brentline hosptial if patient$-$days of $8,800$ are expected for the month of August using each method. Show your calculations.