Calculate R.The multiple R is defined as the correlation between the actual y values and the predicted y values using the new regression equation. The predicted y value using the new equation is represented by the symbol to differentiate from y which represents the actual y values in the data set. We can use our new regression equation from Step 3 to compute predicted program completion time in months for each student using their number of academic degrees prior to enrollment in the RN to BSN Program. For example Student #1 had earned 1 academic degree prior to enrollment and the predicted months to completion for Student 1 is calculated as: y=2.9(1)+16.25 y=13.35
Calculate R.The multiple R is defined as the correlation between the actual y values and the predicted y values using the new regression equation. The predicted y value using the new equation is represented by the symbol to differentiate from y which represents the actual y values in the data set. We can use our new regression equation from Step 3 to compute predicted program completion time in months for each student using their number of academic degrees prior to enrollment in the RN to BSN Program. For example Student #1 had earned 1 academic degree prior to enrollment and the predicted months to completion for Student 1 is calculated as:
y=2.9(1)+16.25
y=13.35
EXERCISE 19Questions to Be Graded
Follow your instructor’s directions to submit your answers to the following questions for grading. Your instructor may ask you to write your answers below and submit them as a hard copy for grading. Alternatively your instructor may ask you to use the space below for notes and submit your answers online at http://evolve.elsevier.com/Grove/Statistics/ under Questions to Be Graded.
Name: _______________________________________________________ Class: _____________________
Date: ___________________________________________________________________________________
1. According to the relevant study results section of the Darling-Fisher etal. (2014) study what categories are reported to be statistically significant?
2. What level of measurement is appropriate for calculating the 2 statistic? Give two examples from Table 2 of demographic variables measured at the level appropriate for 2.
3. What is the 2 for U.S. practice region? Is the 2 value statistically significant? Provide a rationale for your answer.
4. What is the df for provider type? Provide a rationale for why the df for provider type presented in Table 2 is correct.
200
5. 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.
6. State the null hypothesis for provider age in years for RAAPS users and RAAPS nonusers.
7. Should the null hypothesis for provider age in years developed for Question 6 be accepted or rejected? Provide a rationale for your answer.
8. Describe at least one clinical advantage and one clinical challenge of using RAAPS as described by Darling-Fisher etal. (2014).
9. How many null hypotheses are rejected in the Darling-Fisher etal. (2014) study for the results presented in Table 2? Provide a rationale for your answer.
10. A statistically significant difference is present between RAAPS users and RAAPS nonusers for U.S. practice region 2 = 29.68. Does the 2 result provide the location of the difference? Provide a rationale for your answer
(Grove 191-200)
Grove Susan K. Daisha Cipher. Statistics for Nursing Research: A Workbook for Evidence-Based Practice 2nd Edition. Saunders 022016. VitalBook file.
The citation provided is a guideline. Please check each citation for accuracy before use.
Exercise 29
Calculating Simple Linear Regression
Simple linear regression is a procedure that provides an estimate of the value of a dependent variable (outcome) based on the value of an independent variable (predictor). Knowing that estimate with some degree of accuracy we can use regression analysis to predict the value of one variable if we know the value of the other variable (Cohen & Cohen 1983). The regression equation is a mathematical expression of the influence that a predictor has on a dependent variable based on some theoretical framework. For example in Exercise 14 Figure 14-1 illustrates the linear relationship between gestational age and birth weight. As shown in the scatterplot there is a strong positive relationship between the two variables. Advanced gestational ages predict higher birth weights.
A regression equation can be generated with a data set containing subjects’ x and y values. Once this equation is generated it can be used to predict future subjects’ y values given only their x values. In simple or bivariate regression predictions are made in cases with two variables. The score on variable y (dependent variable or outcome) is predicted from the same subject’s known score on variable x (independent variable or predictor).
Research Designs Appropriate for Simple Linear Regression
Research designs that may utilize simple linear regression include any associational design (Gliner etal. 2009). The variables involved in the design are attributional meaning the variables are characteristics of the participant such as health status blood pressure gender diagnosis or ethnicity. Regardless of the nature of variables the dependent variable submitted to simple linear regression must be measured as continuous at the interval or ratio level.
Statistical Formula and Assumptions
Use of simple linear regression involves the following assumptions (Zar 2010):
1. Normal distribution of the dependent (y) variable
2. Linear relationship between x and y
3. Independent observations
4. No (or little) multicollinearity
5. Homoscedasticity
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Data that are homoscedastic are evenly dispersed both above and below the regression line which indicates a linear relationship on a scatterplot. Homoscedasticity reflects equal variance of both variables. In other words for every value of x the distribution of y values should have equal variability. If the data for the predictor and dependent variable are not homoscedastic inferences made during significance testing could be invalid (Cohen & Cohen 1983; Zar 2010). Visual examples of homoscedasticity and heteroscedasticity are presented in Exercise 30.
In simple linear regression the dependent variable is continuous and the predictor can be any scale of measurement; however if the predictor is nominal it must be correctly coded. Once the data are ready the parameters a and b are computed to obtain a regression equation. To understand the mathematical process recall the algebraic equation for a straight line:
y=bx+a
where
y=thedependentvariable(outcome)
x=theindependentvariable(predictor)
b=theslopeoftheline
a=y-intercept(thepointwheretheregressionlineintersectsthey-axis)
No single regression line can be used to predict with complete accuracy every y value from every x value. In fact you could draw an infinite number of lines through the scattered paired values (Zar 2010). However the purpose of the regression equation is to develop the line to allow the highest degree of prediction possiblethe line of best fit. The procedure for developing the line of best fit is the method of least squares. The formulas for the beta () and slope () of the regression equation are computed as follows. Note that once the is calculated that value is inserted into the formula for .
=nxyxynx2(x)2
=ybxn
Hand Calculations
This example uses data collected from a study of students enrolled in a registered nurse to bachelor of science in nursing (RN to BSN) program (Mancini Ashwill & Cipher 2014). The predictor in this example is number of academic degrees obtained by the student prior to enrollment and the dependent variable was number of months it took for the student to complete the RN to BSN program. The null hypothesis is Number of degrees does not predict the number of months until completion of an RN to BSN program.
The data are presented in Table 29-1. A simulated subset of 20 students was selected for this example so that the computations would be small and manageable. In actuality studies involving linear regression need to be adequately powered (Aberson 2010; Cohen 1988). Observe that the data in Table 29-1 are arranged in columns that correspond to 321the elements of the formula. The summed values in the last row of Table 29-1 are inserted into the appropriate place in the formula for b.
TABLE 29-1
ENROLLMENT GPA AND MONTHS TO COMPLETION IN AN RN TO BSN PROGRAM
The computations for the b and are as follows:
Step 1: Calculate b.From the values in Table 29-1 we know that n = 20 x = 20 y = 267 x2 = 30 and xy = 238. These values are inserted into the formula for b as follows:
b=20(238)(20)(267)20(30)202
b=2.9
Step 2: Calculate .From Step 1 we now know that b = 2.9 and we plug this value into the formula for .
=267(2.9)(20)20
=16.25
Step 3: Write the new regression equation:
y=2.9x+16.25
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Step 4: Calculate R.The multiple R is defined as the correlation between the actual y values and the predicted y values using the new regression equation. The predicted y value using the new equation is represented by the symbol to differentiate from y which represents the actual y values in the data set. We can use our new regression equation from Step 3 to compute predicted program completion time in months for each student using their number of academic degrees prior to enrollment in the RN to BSN Program. For example Student #1 had earned 1 academic degree prior to enrollment and the predicted months to completion for Student 1 is calculated as:
y=2.9(1)+16.25
y=13.35
Thus the predicted is 13.35 months. This procedure would be continued for the rest of the students and the Pearson correlation between the actual months to completion (y) and the predicted months to completion () would yield the multiple R value. In this example the R = 0.638. The higher the R the more likely that the new regression equation accurately predicts y because the higher the correlation the closer the actual y values are to the predicted values. Figure 29-1 displays the regression line where the x axis represents possible numbers of degrees and the y axis represents the predicted months to program completion ( values).
FIGURE 29-1 REGRESSION LINE REPRESENTED BY NEW REGRESSION EQUATION.
Step 5: Determine whether the predictor significantly predicts y.
t=Rn21R2
To know whether the predictor significantly predicts y the beta must be tested against zero. In simple regression this is most easily accomplished by using the R value from Step 4:
t=.63820021.407
t=3.52
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The t value is then compared to the t probability distribution table (see Appendix A). The df for this t statistic is n 2. The critical t value at alpha () = 0.05 df = 18 is 2.10 for a two-tailed test. Our obtained t was 3.52 which exceeds the critical value in the table thereby indicating a significant association between the predictor (x) and outcome (y).
Step 6: Calculate R2.After establishing the statistical significance of the R value it must subsequently be examined for clinical importance. This is accomplished by obtaining the coefficient of determination for regressionwhich simply involves squaring the R value. The R2 represents the percentage of variance explained in y by the predictor. Cohen describes R2 values of 0.02 as small 0.15 as moderate and 0.26 or higher as large effect sizes (Cohen 1988). In our example the R was 0.638 and therefore the R2 was 0.407. Multiplying 0.407 100% indicates that 40.7% of the variance in months to program completion can be explained by knowing the student’s number of earned academic degrees at admission (Cohen & Cohen 1983).The R2 can be very helpful in testing more than one predictor in a regression model. Unlike R the R2 for one regression model can be compared with another regression model that contains additional predictors (Cohen & Cohen 1983). The R2 is discussed further in Exercise 30.The standardized beta () is another statistic that represents the magnitude of the association between x and y. has limits just like a Pearson r meaning that the standardized cannot be lower than 1.00 or higher than 1.00. This value can be calculated by hand but is best computed with statistical software. The standardized beta () is calculated by converting the x and y values to z scores and then correlating the x and y value using the Pearson r formula. The standardized beta () is often reported in literature instead of the unstandardized b because b does not have lower or upper limits and therefore the magnitude of b cannot be judged. on the other hand is interpreted as a Pearson r and the descriptions of the magnitude of can be applied as recommended by Cohen (1988). In this example the standardized beta () is 0.638. Thus the magnitude of the association between x and y in this example is considered a large predictive association (Cohen 1988).
. .
The post Calculate R.The multiple R is defined as the correlation between the actual y values and the predicted y values using the new regression equation. The predicted y value using the new equation is represented by the symbol to differentiate from y which represents the actual y values in the data set. We can use our new regression equation from Step 3 to compute predicted program completion time in months for each student using their number of academic degrees prior to enrollment in the RN to BSN Program. For example Student #1 had earned 1 academic degree prior to enrollment and the predicted months to completion for Student 1 is calculated as: y=2.9(1)+16.25 y=13.35 appeared first on academicheroes.com.
Calculate R.The multiple R is defined as the correlation between the actual y values and the predicted y values using the new regression equation. The predicted y value using the new equation is represented by the symbol to differentiate from y which represents the actual y values in the data set. We can use our new regression equation from Step 3 to compute predicted program completion time in months for each student using their number of academic degrees prior to enrollment in the RN to BSN Program. For example Student #1 had earned 1 academic degree prior to enrollment and the predicted months to completion for Student 1 is calculated as: y=2.9(1)+16.25 y=13.35 was first posted on October 19, 2019 at 10:11 pm.
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