Answered: similar size were reported separately…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Cost-to-charge ratios (the percentage of the amount billed that represents the actual cost) for 11 Oregon hospitals of similar size were reported separately for inpatient and outpatient services. The data are shown in the following table.

	Cost-to-charge ratio
Hospital	Inpatient	Outpatient
Blue Mountain	79	63
Curry General	75	67
Good Shepherd	76	62
Grande Ronde	63	50
Harney District	101	53
Lake District	101	74
Pioneer	87	64
St. Anthony	65	57
St. Elizabeth	51	44
Tillamook	55	49
Wallowa Memorial	82	72

(a)

Does there appear to be a strong linear relationship between the cost-to-charge ratio for inpatient and outpatient services? Justify your answer based on the value of the correlation coefficient and examination of a scatterplot of the data. (Round your answer to four decimal places.)

Based on the correlation coefficient value of and the scatterplot, there is relationship between the cost-to-charge ratio for inpatient and outpatient services. Looking at a scatterplot, there .

(b)

Are any unusual features of the data evident in the scatterplot?

Yes. There is no noticeable relationship between inpatient and outpatient cost-to-charge ratios and the points are randomly scattered throughout the graph.

Yes. There are one or more outliers present which alter how well a linear relationship describes the relationship between inpatient and outpatient cost-to-charge ratios.

Yes. There is a noticeable nonlinear relationship between inpatient and outpatient cost-to-charge ratios with the graph suggesting a square root transformation might be appropriate.

Yes. There is a noticeable nonlinear relationship between inpatient and outpatient cost-to-charge ratios with the graph suggesting a reciprocal transformation might be appropriate.

No. There is a moderate linear relationship between inpatient and outpatient cost-to-charge ratios and all the points follow that trend.

(c)

Suppose that the observation for Harney District was removed from the data set. Would the correlation coefficient for the new data set be greater than or less than the one computed in part (a)? Explain.

This point is not an outlier and if it were removed, the linear relationship would be relatively unchanged and the value of r would therefore be approximately the same.

This point is an outlier and if it were removed, the linear relationship would be weaker, and the value of r would therefore be smaller.

This point is not an outlier and if it were removed, the nonlinear relationship would be relatively unchanged and the value of r would therefore be approximately the same.

This point is an outlier and if it were removed, the nonlinear relationship would be stronger, and the value of r would therefore be greater.

This point is an outlier and if it were removed, the linear relationship would be stronger, and the value of r would therefore be greater.

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