The data in the accompanying table represent the rate of returnof a certain company stock for 11​ months, compared with the rateof return of a certain index of 500 stocks. Both are in percent.Complete parts ​(a) through ​(d) below.
Click the icon to view the data table.​(a) Treating the rate ofreturn of the index as the explanatory​ variable, x, use technologyto determine the estimates of
beta 0β0
and
beta 1β1.
The estimate of
beta 0β0
is
nothing.
​(Round to four decimal places as​ needed.)
The estimate of
beta 1β1
is
nothing.
​(Round to four decimal places as​ needed.)
​(b) Assuming the residuals are normally​ distributed, testwhether a linear relation exists between the rate of return of the​index, x, and the rate of return for the company​ stock, y, atthe
alphaαequals=0.10
level of significance. Choose the correct answer below.
State the null and alternative hypotheses.
A.
Upper H 0H0​:
beta 1β1equals=0
Upper H 1H1​:
beta 1β1greater than>0
B.
Upper H 0H0​:
beta 1β1equals=0
Upper H 1H1​:
beta 1β1not equals≠0
C.
Upper H 0H0​:
beta 0β0equals=0
Upper H 1H1​:
beta 0β0not equals≠0
D.
Upper H 0H0​:
beta 0β0equals=0
Upper H 1H1​:
beta 0β0greater than>0
Determine the​ P-value for this hypothesis test.
​P-valueequals=nothing
​(Round to three decimal places as​ needed.) State theappropriate conclusion at the
alphaαequals=0.10
level of significance. Choose the correct answer below.
A.Reject
Upper H 0H0.
There is not sufficient evidence to conclude that a linearrelation exists between the rate of return of the index and therate of return of the company stock.  
B.Reject
Upper H 0H0.
There is sufficient evidence to conclude that a linear relationexists between the rate of return of the index and the rate ofreturn of the company stock.
C.Do not reject
Upper H 0H0.
There is not sufficient evidence to conclude that a linearrelation exists between the rate of return of the index and therate of return of the company stock.  
D.Do not reject
Upper H 0H0.
There is sufficient evidence to conclude that a linear relationexists between the rate of return of the index and the rate ofreturn of the company stock.
​(c) Assuming the residuals are normally​ distributed, constructa​ 90% confidence interval for the slope of the true​ least-squaresregression line.
Lower​ bound:
nothing
​(Round to four decimal places as​ needed.) Upper​ bound:
nothing
​(Round to four decimal places as​ needed.) ​(d) What is themean rate of return for the company stock if the rate of return ofthe index is
3.153.15​%?
The mean rate of return for the company stock if the rate ofreturn of the index is
3.153.15​%
is
nothing​%.
​(Round to three decimal places as​ needed.)
Click to select your answer(s).
Rate of Return
Month | Rates of return of the​index, x | Rates of return of the company​ stock, y | |
|---|
​Apr-07 | 4.334.33             | 3.283.28             | |
​May-07 | 3.253.25             | 5.095.09             | |
​Jun-07 | negative 1.78−1.78             | 0.540.54             | |
​Jul-07 | negative 3.20−3.20             | 2.882.88             | |
​Aug-07 | 1.291.29             | 2.692.69             | |
​Sept-07 | 3.583.58             | 7.417.41             | |
​Oct-07 | 1.481.48             | negative 4.83−4.83             | |
​Nov-07 | negative 4.40−4.40             | negative 2.38−2.38             | |
​Dec-07 | negative 0.86−0.86             | 2.372.37             | |
​Jan-08 | negative 6.12−6.12             | negative 4.27−4.27             | |
​Feb-08 | negative 3.48−3.48             | negative 3.77−3.77             | |
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