/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 18 The relationship between hospita... [FREE SOLUTION] | 91影视

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Chapter 5: Problem 18

The relationship between hospital patient-tonurse ratio and various characteristics of job satisfaction and patient care has been the focus of a number of research studies. Suppose \(x=\) patient-to-nurse ratio is the predictor variable. For each of the following potential dependent variables, indicate whether you expect the slope of the least-squares line to be positive or negative and give a brief explanation for your choice. a. \(y=\) a measure of nurse's job satisfaction (higher values indicate higher satisfaction) b. \(y=\) a measure of patient satisfaction with hospital care (higher values indicate higher satisfaction) c. \(y=\) a measure of patient quality of care.

Short Answer

Expert verified
For all three scenarios (nurse's job satisfaction, patient satisfaction with hospital care, and patient quality of care), it's expected that the slope of the least-squares line will be negative. The reason being, higher patient-to-nurse ratio likely lead to decreased job satisfaction for nurses and potentially lower quality of care and satisfaction for patients.

Step by step solution

01

Understanding Scenario a: nurse's job satisfaction

In the first scenario, the dependent variable \(y\) is a measure of nurse's job satisfaction, where higher values indicate higher satisfaction. It's reasonable to expect that as the patient-to-nurse ratio (predictor variable \(x\)) increases, nurse's job satisfaction would decrease. It implies the more patients a nurse is required to care for, the greater the workload, potentially leading to less job satisfaction. Hence, you could expect a negative slope for the least-squares line.
02

Understanding Scenario b: patient satisfaction with hospital care

In the second scenario, the dependent variable \(y\) is a measure of patient satisfaction with hospital care, where higher values indicate higher satisfaction. Similar to Step 1, as the patient-to-nurse ratio increases, it could be expected that each nurse has less time and attention for each patient, potentially decreasing patient satisfaction with hospital care. Therefore, the slope of the least-squares line would likely be negative.
03

Understanding Scenario c: patient quality of care

In the final scenario, the dependent variable \(y\) is a measure of patient quality of care. You would anticipate that increasing patient-to-nurse ratio might result in lower quality of care for patients, as nurses might not have enough time to devote to each patient. Thus, a negative slope for the least-squares line may also be anticipated for this scenario.

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Most popular questions from this chapter

Researchers have examined a number of climatic variables in an attempt to understand the mechanisms that govern rainfall runoff. The paper "The Applicability of Morton's and Penman's Evapotranspiration Estimates in Rainfall-Runoff Modeling" (Water 91影视 Bulletin [1991]: \(611-620\) ) reported on a study that examined the relationship between \(x=\) cloud cover index and \(y=\) sunshine index. The cloud cover index can have values between 0 and \(1 .\) The accompanying data are consistent with summary quantities in the article. The authors of the article used a cubic regression to describe the relationship between cloud cover and sunshine. \begin{tabular}{cc} Cloud Cover Index \((x)\) & Sunshine Index \((y)\) \\ \hline \(0.2\) & \(10.98\) \\ \(0.5\) & \(10.94\) \\ \(0.3\) & \(10.91\) \\ \(0.1\) & \(10.94\) \\ \(0.2\) & \(10.97\) \\ \(0.4\) & \(10.89\) \\ \(0.0\) & \(10.88\) \\ \(0.4\) & \(10.92\) \\ \(0.3\) & \(10.86\) \\ \hline \end{tabular} a. Construct a scatterplot of the data. What characteristics of the plot suggest that a cubic regression would be more appropriate for summarizing the relationship between sunshine index and cloud cover index than a linear or quadratic regression? b. Find the equation of the least-squares cubic function. c. Construct a residual plot by plotting the residuals from the cubic regression model versus \(x\). Are there any troubling patterns in the residual plot that suggest that a cubic regression is not an appropriate way to summarize the relationship? d. Use the cubic regression to predict sunshine index when the cloud cover index is \(0.25\). e. Use the cubic regression to predict sunshine index when the cloud cover index is \(0.45\). f. Explain why it would not be a good idea to use the cubic regression equation to predict sunshine index for a cloud cover index of \(0.75\).

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The following quote is from the paper "Evaluation of the Accuracy of Different Methods Used to Estimate Weights in the Pediatric Population" (Pediatrics [2009 ]: el045-elo51): As expected, the model demonstrated that weight increased with age, but visual inspection of an age versus weight plot demonstrated a nonlinear relationship unless infants and children were analyzed separately. The linear coefficient for age as a predictor of weight was \(6.93\) in infants and \(3.1\) to \(3.48\) in children. This quote suggests that when a scatterplot of weight versus age was constructed for all 1011 children in the study described in the paper, the relationship between \(y=\) weight and \(x=\) age was not linear. When the 1011 children were separated into two groups-infants (age birth to 1\. year) and children (age 1 to 10 years) - and separate scatterplots were constructed, the relationship between weight and age appeared linear in each scatterplot. The slopes reported in the given quote (referred to as "the linear coefficient") are expressed in kg/year. Briefly explain why the relationship between weight and age in the scatterplot for the combined group would appear nonlinear.

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