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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 GradedFollow 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 https://allaplusessays.com/order 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.2005. 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 29Calculating Simple Linear RegressionSimple
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 RegressionResearch 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
AssumptionsUse of simple linear regression involves the following
assumptions (Zar 2010):1. Normal distribution of the dependent (y)
variable2. Linear relationship between x and y3. Independent
observations4. No (or little) multicollinearity5.
Homoscedasticity320Data 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
wherey=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 CalculationsThis 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
29-1ENROLLMENT 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
322Step 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
323The 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).
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