Question

# Profitability remains a challenge for banks and thrifts with less than​ \$2 billion of assets. The...

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 203 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. A multiple linear regression model resulted in an SSR of 7.61 and an SSE of 123.24. Complete parts​ (a) through​ (d) below.

a. Determine whether there is a significant relationship between ROA and the two independent variables​ (used efficiency ratio and total​ risk-based capital) at the

0.05 level of significance.

What are the correct hypotheses to​ test?

Ho: (at least one Beta j cannot equal 0, j=1,2,3), (Beta1=Beta2=Beta3=0), (Beta1=Beta2=0), (at least one Beta j cannot equal 0,j=0,1), (at least one Beta j cannot equal 0,j=1,2), (Beta0=Beta1=Beta2=0)

H1:(at least one Beta j cannot equal 0, j=1,2,3), (Beta1=Beta2=Beta3=0), (Beta1=Beta2=0), (at least one Beta j cannot equal 0,j=0,1), (at least one Beta j cannot equal 0,j=1,2), (Beta0=Beta1=Beta2=0)

Calculate the test statistic:

Determine the p value:

State the conclusion:

Since the p-value is (greater or less) than the level of significance, (reject, do not reject) the null hypothesis. There is (sufficient, insufficient) evidence to conclude there is a linear relationship.

b: Interpret the meaning of the p-value. Choose the correct answer below.

A.The​p-value is the probability that there is a linear relationship between the two independent variables.

B. The​ p-value is the probability of getting an overall test statistic equal to or less than the sample​ result, assuming there is no linear relationship between the dependent variable and the independent variables.

C. The​ p-value is the probability that there is a linear relationship between the dependent variable and at least one of the independent variables.

D. The​ p-value is the probability of getting an overall test statistic equal to or greater than the sample​ result, assuming there is no linear relationship between the dependent variable and the independent variables.

c. Comput the coefficient of multiple determination, r2, and interpret its meaning

r2=

Interpret the meaning of r2

The coefficient of multiple determination indicates that _% of the variation in (effiecieny ratio, effiecieny ratio and captial, capital, ROA) can be explained by the variation in (effiecieny ratio, effiecieny ratio and captial, capital, ROA)

(a)

Ho: (Beta1=Beta2=0)

H1: (at least one Beta j cannot equal 0,j=1,2)

Calculate the test statistic: 6.176

Determine the p value: 0.0025

State the conclusion:

Since the p-value is ( less) than the level of significance, (reject) the null hypothesis. There is (sufficient) evidence to conclude there is a linear relationship.

(b) D. The​ p-value is the probability of getting an overall test statistic equal to or greater than the sample​ result, assuming there is no linear relationship between the dependent variable and the independent variables.

(c) r2= 0.058

The coefficient of multiple determination indicates that 5.8% of the variation in (ROA) can be explained by the variation in (effiecieny ratio and captial)

 Source SS df MS F p-value Regression 7.61 2 3.805 6.176447 0.002496 Residual 123.21 200 0.61605 Total 130.82 202

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