Below is a partial data for selected health care systems (n=18) showing each hea

Question

Below is a partial data for selected health care systems (n=18) showing each health care system’s operating margin (computed as total revenue minus total expenses divided by total revenue plus net operating profits) and percent of equity financing (fund balance divided by total assets). Use the scatter plot below to answer the following questions:

The correlation between the response variable and the predictor variable could be best described as:

a.     Perfectly positively linear

b.     Perfectly negatively linear

c.     Positively correlated

d.     Negatively correlated

e.     No correlation exists

What is the response variable in this problem?

Percent of Equity Financing

Percent Operating Margin

What is the predictor variable in this problem?

Percent of Equity Financing

Percent Operating Margin

Given the regression model, for every percentage point increase in a health care company’s equity financing, by how many percentage points does operating margin increase?

-7.9356

0.2736

0.6759

0.8221

None of the above

How much variability in the response variable can be explained by the independent variable?

a.         -7.9356

b.         0.2736

c.         0.6759

d.         0.8221

e.         None of the above

Blue Shield Health Systems has 40 percent equity financing. What is the expected percent operating margin for BSSH?

-7.9356

0.2736

0.6759

0.8221

None of the above

How much variability in the response variable can be explained by the independent variable? -7.9356 0.2736 0.6759 0.8221 None of the above BIue Shield Health Systems has 40 percent equity financing. What is the expected percent operating margin for BSSH -7.9356 0.2736 0.6759 0.8221 None of the above

Explanation / Answer

Response variable in the problem is Percent Operating Margin.

Predictor variable in the problem is Percent Equity Financing.

As the regression equation is y=0.2736x-7.9356, i.e. the coefficient of x or the slope of the regression line is 0.2736 > 0. so the correlation between predictor and response variable is positive.

For every percentage point increase in a health care company’s equity financing, percentage points does operating margin increase = (0.2736*(x+1)-7.9356) - (0.2736*x-7.9356) = 0.2736

Fraction of variability in the response variable can be explained by the independent variable = R2 = 0.6759

If Blue Shield Health Systems has 40 percent equity financing. so expected percent operating margin for BSSH

= 0.2736*40-7.9356 = 3.0084.

So the answer is None of the above.

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