Question

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.**Thep-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)

Answer #1

(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 |

A multiple linear regression model based on a sample of 17 weeks
is developed to predict standby hours based on the total staff
present and remote hours. The SSR is 20,905.02 and the SSE is
25,434.29. (use 0.05 level of significance)
H0: B1 = B2 = 0
H1: At least one Bj does not equal 0, j = 1, 2
1. Calculate the test statistic.
Fstat= _____
2. Find the p-value.
p-value= _____
3. Compute the coefficient of multiple determination,...

Question 1
How is a residual calculated in a regression model? i.e. what is
the meaning of a residual?
a)The difference between the actual value, y, and the fitted
value, y-hat
b)The difference between the fitted value, y-hat, and the mean,
y-bar
c)The difference between the actual value, y, and the mean,
y-ba
d)The square of the difference between the fitted value, y-hat,
and the mean, y-bar
Question 2
Larger values of r-squared imply that the observations are more
closely...

1. In a multiple
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b0 = -10 b1
= 4.5 b2 = -6.0
a. Write the
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b Suppose a
sample of 25 observations produces this result, SSE = 480. What is
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Y = 12 + 6X1 -- 3 X2
Determine which of the following
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1. For a pair of sample x- and y-values, what is the difference
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variable
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"Risk' can be best defined as on the of the
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a. Variability of returns and probability of financial loss
b. Chance of financial loss
c. Variability of returns
d. Correlation of relationship among two variables
Which of the following statement is NOT TRUE when we argue that
the idea of riskless arbitrage is to accumulate the portfolio with
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a. Requires no net wealth invested initially
b. Invest in the long-term securities only where risk will be...

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is the time to consult with your business, financial, and legal
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Outside advisers are impartial and are more likely to see the bad
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