Question

The manager of the main laboratory facility at Elmhurst HealthElmhurst Health Center is interested in being able to predict the overhead costs each month for the lab. The manager believes that total overhead varies with the number of lab tests performed but that some costs remain the same each month regardless of the number of lab tests performed. The lab manager collected the following data for the first seven months of the year.
Requirements

1.

Determine the​ lab's cost equation​ (use the output from the Excel​ regression).

2.

Determine the​ R-square (use the output from the Excel​regression).

3.

Predict the total laboratory overhead for the month if 3,100 tests are performed

Data Table

Number of Lab Tests

Total Laboratory

Month

Performed

Overhead Costs

January. . . . . . . . .

3,000

$21,900

February. . . . . . . .

2,850

$20,600

March. . . . . . . . . . .

3,400

$28,900

April. . . . . . . . . . . .

3,700

$31,000

May. . . . . . . . . . . .

3,900

$28,000

June. . . . . . . . . . . .

1,900

$20,200

July. . . . . . . . . . . .

2,050

$14,000

The laboratory manager performed a regression analysis to predict total laboratory overhead costs. The output generated by Excel is as​ follows:

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.878214

R Square

0.77126

Adjusted R Square

0.725512

Standard Error

3156.338706

Observations

7

ANOVA

df

SS

MS

F

Significance F

Regression

1

167956201.3

167956201.3

16.858885

0.009301

Residual

5

49812370.15

9962474.03

Total

6

217768571.4

Standard

Lower

Upper

Coefficients

Error

t Stat

P-value

95%

95%

Intercept

3187.94

5092.169

0.626

0.559

-9901.898

16277.778

X Variable 1

6.84

1.666

4.106

0.009

2.558

11.123

Answer 1

Answer:

1.  Lab's cost= 3187.94 +6.84 number of lab test performed

2. 0.77126

3. $24391.94

Explanation:

1.

The Lab's cost depends on the number of lab test performed. So, Lab's cost is a dependent variable while number of lab test is an independent variable. The linear regression equation is written as

Y= a+bx

Where,

y= dependent variable

x= independent variable

a= intercept

b= slope

So, the equation can be written as

Lab's cost= a+b number of lab test performed

From the Excel output we know that

Intercept = a= 3187.94

Slope= b =6.84

So, the required regression equation is

Lab's cost= 3187.94 +6.84 number of lab test performed

2.

The Excel output shows that R-square is 0.77126. R²=0.77126 means that only 77.13% of variation in Lab's cost is explained by its linear relationship with number of lab test performed.

3.

We have to predict the lab's cost for 3100 test.

We know that

Lab's cost= 3187.94 +6.84 number of lab test performed.

Here, number of lab test performed=3100.

So,

Lab's cost= 3187.94 +6.84(3100)

Lab's cost= 3187.94 +21204

Lab's cost=$24391.94

Thus, the predicted total laboratory overhead for the month if 3,100 tests are performed is $24391.94.