Profitability remains a challenge for banks and thrifts with less than​ $2 billion of assets. The business problem facing a bank analyst relates to the factors that affect return on assets​ (ROA), an indicator of how profitable a company is relative to its total assets. Data collected from a sample of 88 community banks include the ROA​ (%), the efficiency ratio​ (%), as a measure of bank productivity​ (the lower the efficiency​ ratio, the​ better), and total​ risk-based capital​ (%), as a measure of capital adequacy. Use the accompanying multiple linear regression results to complete parts​ (a) and​ (b) below. Variable Coefficient Standard Error t Statistic ​p-value   Intercept −0.21762   0.39401 −0.55      0.5822   Efficiency​ Ratio, X1 0.01443   0.00498 2.90      0.0048 ​ Risk-Based Capital, X2 0.04002   0.01034 3.87      0.0002   Find the test statistic for X1.   tSTAT=______ ​(Type an integer or a decimal. Do not​ round.)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section4.5: Correlation And Causation
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Profitability remains a challenge for banks and thrifts with less than​ $2 billion of assets. The business problem facing a bank analyst relates to the factors that affect return on assets​ (ROA), an indicator of how profitable a company is relative to its total assets. Data collected from a sample of
88
community banks include the ROA​ (%), the efficiency ratio​ (%), as a measure of bank productivity​ (the lower the efficiency​ ratio, the​ better), and total​ risk-based capital​ (%), as a measure of capital adequacy. Use the accompanying multiple linear regression results to complete parts​ (a) and​ (b) below.
Variable
Coefficient
Standard Error
t Statistic
​p-value
  Intercept
−0.21762  
0.39401
−0.55     
0.5822
  Efficiency​ Ratio, X1
0.01443  
0.00498
2.90     
0.0048
​ Risk-Based Capital, X2
0.04002  
0.01034
3.87     
0.0002

 

Find the test statistic for
X1.
 
tSTAT=______
​(Type an integer or a decimal. Do not​ round.)
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