A sample of n = 20 hospitals was selected, and the values of y = monthly labor-hours and k = 15 workload variables (items that result in need for personnel in a hospital such as X- ray exposures and length of patient's stay) were determined. The goal here is to produce a regression equation that will estimate (or predict) personnel needs for hospitals. When the multiple regression model using these 15 predictors was fit to the data, R = 0.94 resulted. (1) Does the model appear to specify a useful relationship between y and the predictor variables? Carry out a test using significance level 0.05. [Hint: State the hypotheses, calculate the F ratio, compare to the F critical value, draw conclusion.] (2) Based on the result of part (1), does a high R2 value by itself imply that a model is useful? Under what circumstances might you be suspicious of a model with a high R value? (3) Calculate Rdj (4) After deleting 12 variables, we fit the model with just 3 predictors I = monthly X-ray exposures, r2 = monthly occupied bed-days, 13 = average length of patient's stay, in days. The estimated regression equation is ý = 2000 + 0.03.r1 +1.08r2- 440r3 R remains the same. In addition, MSE = 100,000, the estimated standard error of Bi is 0.012. Calculate and interpret a 90% CI for B1. (5) Using the model from (4), a 95% CI for the true average monthly labor-hours when a = 1000, r2 = 500, and r3 4 is calculated to be [492, 1128]. Compute a 95% PI for the monthly labor-hours of a new hospital with r = 1000, r2 = 500, and ra = 4.
A sample of n = 20 hospitals was selected, and the values of y = monthly labor-hours and k = 15 workload variables (items that result in need for personnel in a hospital such as X- ray exposures and length of patient's stay) were determined. The goal here is to produce a regression equation that will estimate (or predict) personnel needs for hospitals. When the multiple regression model using these 15 predictors was fit to the data, R = 0.94 resulted. (1) Does the model appear to specify a useful relationship between y and the predictor variables? Carry out a test using significance level 0.05. [Hint: State the hypotheses, calculate the F ratio, compare to the F critical value, draw conclusion.] (2) Based on the result of part (1), does a high R2 value by itself imply that a model is useful? Under what circumstances might you be suspicious of a model with a high R value? (3) Calculate Rdj (4) After deleting 12 variables, we fit the model with just 3 predictors I = monthly X-ray exposures, r2 = monthly occupied bed-days, 13 = average length of patient's stay, in days. The estimated regression equation is ý = 2000 + 0.03.r1 +1.08r2- 440r3 R remains the same. In addition, MSE = 100,000, the estimated standard error of Bi is 0.012. Calculate and interpret a 90% CI for B1. (5) Using the model from (4), a 95% CI for the true average monthly labor-hours when a = 1000, r2 = 500, and r3 4 is calculated to be [492, 1128]. Compute a 95% PI for the monthly labor-hours of a new hospital with r = 1000, r2 = 500, and ra = 4.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter1: Functions
Section1.CR: Chapter 1 Review
Problem 86CR
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![A sample of n = 20 hospitals was selected, and the values of y = monthly labor-hours and
k = 15 workload variables (items that result in need for personnel in a hospital such as X-
ray exposures and length of patient's stay) were determined. The goal here is to produce
a regression equation that will estimate (or predict) personnel needs for hospitals. When
the multiple regression model using these 15 predictors was fit to the data, R = 0.940
resulted.
(1) Does the model appear to specify a useful relationship between y and the predictor
variables? Carry out a test using significance level 0.05.
[Hint: State the hypotheses, calculate the F ratio, compare to the F critical value,
draw conclusion.]
(2) Based on the result of part (1), does a high R? value by itself imply that a model is
useful? Under what circumstances might you be suspicious of a model with a high
R value?
(3) Calculate Radj
(4) After deleting 12 variables, we fit the model with just 3 predictors
Ti = monthly X-ray exposures,
12 = monthly occupied bed-days,
I3 = average length of patient's stay, in days.
%3D
The estimated regression equation is
ŷ = 2000 + 0.03.r1 +1.08r2 – 440r3
R remains the same. In addition, MSE = 100,000, the estimated standard error of
Bi is 0.012. Calculate and interpret a 90% CI for B1.
(5) Using the model from (4), a 95% CI for the true average monthly labor-hours when
T1 = 1000, r2 = 500, and r3 = 4 is calculated to be [492, 1128]. Compute a 95% PI
for the monthly labor-hours of a new hospital with r1 = 1000, r2 = 500, and r3 = 4.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0df43032-4a38-4e14-ba56-039065cf4a5e%2Fd496cb01-4a06-4127-9b93-b5d734fbea62%2Fxc7dpv9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A sample of n = 20 hospitals was selected, and the values of y = monthly labor-hours and
k = 15 workload variables (items that result in need for personnel in a hospital such as X-
ray exposures and length of patient's stay) were determined. The goal here is to produce
a regression equation that will estimate (or predict) personnel needs for hospitals. When
the multiple regression model using these 15 predictors was fit to the data, R = 0.940
resulted.
(1) Does the model appear to specify a useful relationship between y and the predictor
variables? Carry out a test using significance level 0.05.
[Hint: State the hypotheses, calculate the F ratio, compare to the F critical value,
draw conclusion.]
(2) Based on the result of part (1), does a high R? value by itself imply that a model is
useful? Under what circumstances might you be suspicious of a model with a high
R value?
(3) Calculate Radj
(4) After deleting 12 variables, we fit the model with just 3 predictors
Ti = monthly X-ray exposures,
12 = monthly occupied bed-days,
I3 = average length of patient's stay, in days.
%3D
The estimated regression equation is
ŷ = 2000 + 0.03.r1 +1.08r2 – 440r3
R remains the same. In addition, MSE = 100,000, the estimated standard error of
Bi is 0.012. Calculate and interpret a 90% CI for B1.
(5) Using the model from (4), a 95% CI for the true average monthly labor-hours when
T1 = 1000, r2 = 500, and r3 = 4 is calculated to be [492, 1128]. Compute a 95% PI
for the monthly labor-hours of a new hospital with r1 = 1000, r2 = 500, and r3 = 4.
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