Understanding Simple Linear Regression

1. According to the study narrative and Figure 1 in the Flannigan et al. (2014) study, does the APLS UK formulae under- or overestimate the weight of children younger than 1 year of age? Provide a rationale for your answer.

2. Using the values a = 3.161 and b = 0.502 with the novel formula in Figure 1, what is the predicted weight in kilograms (kg) for a child at 9 months of age? Show your calculations.

3. Using the values a = 3.161 and b = 0.502 with the novel formula in Figure 1, what is the predicted weight in kilograms for a child at 2 months of age? Show your calculations.

4. In Figure 2, the formula for calculating y (weight in kg) is Weight in kg = (0.176 × age in months) + 7.241. Identify the y intercept and the slope in this formula.

5. Using the values a = 7.241 and b = 0.176 with the novel formula in Figure 2, what is the predicted weight in kilograms for a child 3 years of age? Show your calculations.

6. Using the values a = 7.241 and b = 0.176 with the novel formula in Figure 2, what is the predicted weight in kilograms for a child 5 years of age? Show your calculations.

7. In Figure 3, some of the actual mean weights represented by the blue line with squares are above the dotted straight line for the novel formula, but others are below the straight line. Is this an expected finding? Provide a rationale for your answer.

8. In Figure 3, the novel formula is (Weight in kilograms = (0.331 × Age in months) – 6.868. What is the predicted weight in kilograms for a child 10 years old? Show your calculations.

9. Was the sample size of this study adequate for conducting simple linear regression? Provide a rationale for your answer.

10. Describe one potential clinical advantage and one potential clinical problem with using the three novel formulas presented in Figures 1, 2, and 3 in a PICU setting.

According to the relevant study results section of the Darling-Fisher et al. (2014) study, what categories are reported to be statistically significant?

What level of measurement is appropriate for calculating the χ2 statistic? Give two exam¬ples from Table 2 of demographic variables measured at the level appropriate for χ2.

What is the χ2 for U.S. practice region? Is the χ2 value statistically significant? Provide a rationale for your answer.

What is the df for provider type? Provide a rationale for why the df for provider type pre¬sented in Table 2 is correct.

Is there a statistically significant difference for practice setting between the Rapid Assessment for Adolescent Preventive Services (RAAPS) users and nonusers? Provide a rationale for your answer.

State the null hypothesis for provider age in years for RAAPS users and RAAPS nonusers.

Should the null hypothesis for provider age in years developed for Question 6 be accepted or rejected? Provide a rationale for your answer.

Describe at least one clinical advantage and one clinical challenge of using RAAPS as described by Darling-Fisher et al. (2014).

How many null hypotheses are rejected in the Darling-Fisher et al. (2014) study for the results presented in Table 2? Provide a rationale for your answer.

A statistically significant difference is present between RAAPS users and RAAPS nonusers for U.S. practice region, χ2 = 29.68. Does the χ2 result provide the location of the difference? Provide a rationale for your answer.

If you have access to SPSS, compute the Shapiro-Wilk test of normality for the variable age (as demonstrated in Exercise 26). If you do not have access to SPSS, plot the frequency distributions by hand. What do the results indicate? See Chart

Tests of Normality
Kolmogorov-Smirnova Shapiro-Wilk
Statistic df Sig. Statistic df Sig.
Age .140 20 .200* .949 20 .357
Number of Months to Complete Program .159 20 .200* .931 20 .160
*. This is a lower bound of the true significance.
a. Lilliefors Significance Correction

State the null hypothesis where age at enrollment is used to predict the time for comple¬tion of an RN to BSN program.

What is b as computed by hand (or using SPSS)? See Chart – .047

Coefficientsa
Model Unstandardized Coefficients Standardized Coefficients t Sig.
B Std. Error Beta
1 (Constant) 11.763 3.536 3.326 .004
Age .047 .102 .108 .459 .651
a. Dependent Variable: Number of Months to Complete Program

4. What is a as computed by hand (or using SPSS)? See Chart – 11.763

5. Write the new regression equation.

Y=bx+a

6. How would you characterize the magnitude of the obtained R2 value? Provide a rationale for your answer. See Chart
R Square .012

Model Summary
Model R R Square Adjusted R Square Std. Error of the Estimate
1 .108a .012 -.043 3.368
a. Predictors: (Constant), Age

7. How much variance in months to RN to BSN program completion is explained by knowing the student’s enrollment age?

8. What was the correlation between the actual y values and the predicted y values using the new regression equation in the example? See Chart
R .108

9. Write your interpretation of the results as you would in an APA-formatted journal.

10. Given the results of your analyses, would you use the calculated regression equation to predict future students’ program completion time by using enrollment age as x? Provide a rationale for your answer.

 

 

 

 

 

 

 

 

Sample Solution

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