i) Based on the output given, use these data to develop the equation of the regression model to predict the number of business bankruptcies by the number of firm births. i) Explain the values of r and r. ii) Predict the number of business bankruptcies if the number of firm births is 54.0 (10,000s). iv) Do the data support the existence of a linear relationship between the number of firm births and the number of business bankruptcies? Test using a = 0.05.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
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Chapter10: Statistics
Section10.6: Summarizing Categorical Data
Problem 23PPS
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Is it possible to predict the annual number of business bankruptcies by the number of
firm births (business starts) in the United States? The following data published by the
U.S. Small Business Administration, Office of Advocacy, are pairs of the number of
business bankruptcies (1,000s) and the number of firm births (10,000s) for a six-year
period.
Business Bankruptcies
(1,000)
34.3
Firm Births
(10,000)
58.1
35.0
55.4
38.5
57.0
40.1
58.5
35.5
57.4
37.9
58.0
i) Based on the output given, use these data to develop the equation of the
regression model to predict the number of business bankruptcies by the
number of firm births.
ii) Explain the values of r and r.
iii) Predict the number of business bankruptcies if the number of firm births is
54.0 (10,000s).
iv) Do the data support the existence of a linear relationship between the number
of firm births and the number of business bankruptcies? Test using a = 0.05.
OUTPUT
Model Summary
Std. Error of the
Estimate
Adusted R
Model
R
R Square
Square
428
183
021
2.30962
a. Predictors: (Constant), FIRM_BIRTHS
ANOVA
Model
Sum of Squares
Mean Square
df
Sig
Regression
4.793
4.793
899
397
Residual
21.335
4
5.334
Total
26. 128
a. Dependent Variable: B_BANKRUPTCIES
b. Predictors: (Constant), FIRM_BIRTHS
Coeficients
Standardized
Coefficients
Unstandardized Coeficients
Std. Eror
Model
Beta
Sin
(Constant)
FIRM BIRTHS
-13.503
53.163
254
812
878
926
428
948
397
a. Dependent Variable: B_BANKRUPTCIES
Transcribed Image Text:Is it possible to predict the annual number of business bankruptcies by the number of firm births (business starts) in the United States? The following data published by the U.S. Small Business Administration, Office of Advocacy, are pairs of the number of business bankruptcies (1,000s) and the number of firm births (10,000s) for a six-year period. Business Bankruptcies (1,000) 34.3 Firm Births (10,000) 58.1 35.0 55.4 38.5 57.0 40.1 58.5 35.5 57.4 37.9 58.0 i) Based on the output given, use these data to develop the equation of the regression model to predict the number of business bankruptcies by the number of firm births. ii) Explain the values of r and r. iii) Predict the number of business bankruptcies if the number of firm births is 54.0 (10,000s). iv) Do the data support the existence of a linear relationship between the number of firm births and the number of business bankruptcies? Test using a = 0.05. OUTPUT Model Summary Std. Error of the Estimate Adusted R Model R R Square Square 428 183 021 2.30962 a. Predictors: (Constant), FIRM_BIRTHS ANOVA Model Sum of Squares Mean Square df Sig Regression 4.793 4.793 899 397 Residual 21.335 4 5.334 Total 26. 128 a. Dependent Variable: B_BANKRUPTCIES b. Predictors: (Constant), FIRM_BIRTHS Coeficients Standardized Coefficients Unstandardized Coeficients Std. Eror Model Beta Sin (Constant) FIRM BIRTHS -13.503 53.163 254 812 878 926 428 948 397 a. Dependent Variable: B_BANKRUPTCIES
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