The data in the accompanying table represent the rate of return of a certain company stock for 11 months, compared with the rate of return of a certain index of 500 stocks. Both are in percent. Complete parts (a) through (d) below.E Click the icon to view the data table.(a) Treating the rate of return of the index as the explanatory variable, x, use technology to determine the estimates of ßn and B,.The estimate of ßo isO.(Round to four decimal places as needed.)The estimate of B, is(Round to four decimal places as needed.)(b) Assuming the residuals are normally distributed, test whether a linear relation exists between the rate of return of the index, x, and the rate of return for the companv stock v at the a=0 10 level of significance Choose theanswer below.O Rate of Return- XState the null and alternative hypotheses.O A. Ho: Po =0H,: Bo #0MonthRates of return of the Rates of return of the eindex, x4.23company stock, y3.38O B. Ho: Po = 0H;: Po >0Apr-18May-183.255.09- 1.78- 3.20Jun-180.54OC. Ho: B1 =0H;: B, #0Jul-18Aug-18Sept-18Oct-18Nov-18Dec-18Jan-19Feb-192.882.691.293.587.41O D. Ho: P1 =0H;: P, > 0- 4.83- 2.381.48- 4.40- 0.86- 6.122.37- 4.27- 3.77Determine the P-value for this hypothesis test.- 3.48P-value =D (Round to three decimal places as needed.)State the appropriate conclusion at the a = 0.10 level of significance. Choose the correct answer below.PrintDoneO A. Reject H.. There is sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate of return of the company stock.O B. Do not reject H,. There is sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate of return of the company stock.OC. Do not reject Hp. There is not sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate of return of the company stockO D. Reject H.. There is not sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate of return of the company stock. (c) Assuming the residuals are normally distributed, construct a 90% confidence interval for the slope of the true least-squares regression line.| (Round to four decimal places as needed.)Upper bound: O (Round to four decimal places as needed.)Lower bound:(d) What is the mean rate of return for the company stock if the rate of return of the index is 3.45%?The mean rate of return for the company stock if the rate of return of the index is 3.45% is %.(Round to three decimal places as needed.)

Regression analysis is done with the help of EXCEL software. The procedure is as follows. Enter the…

(c) Assuming the residuals are normally distributed, construct a 90% confidence interval for the slope of the true least-squares regression line. Lower bound: | (Round to four decimal places as needed.) ] (Round to four decimal places as needed.) Upper bound: (d) What is the mean rate of return for the company stock if the rate of return of the index is 3.45%? The mean rate of return for the company stock if the rate of return of the index is 3.45% is %. (Round to three decimal places as needed.)

(c) Assuming the residuals are normally distributed, construct a 90% confidence interval for the slope of the true least-squares regression line. Lower bound: | (Round to four decimal places as needed.) ] (Round to four decimal places as needed.) Upper bound: (d) What is the mean rate of return for the company stock if the rate of return of the index is 3.45%? The mean rate of return for the company stock if the rate of return of the index is 3.45% is %. (Round to three decimal places as needed.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

Question

The data in the accompanying table represent the rate of return of a certain company stock for 11 months, compared with the rate of return of a certain index of 500 stocks. Both are in percent. Complete parts (a) through (d) below.
E Click the icon to view the data table.
(a) Treating the rate of return of the index as the explanatory variable, x, use technology to determine the estimates of ßn and B,
.
The estimate of ßo isO.
(Round to four decimal places as needed.)
The estimate of B, is
(Round to four decimal places as needed.)
(b) Assuming the residuals are normally distributed, test whether a linear relation exists between the rate of return of the index, x, and the rate of return for the companv stock v at the a=0 10 level of significance Choose the
answer below.
O Rate of Return
- X
State the null and alternative hypotheses.
O A. Ho: Po =0
H,: Bo #0
Month
Rates of return of the Rates of return of the e
index, x
4.23
company stock, y
3.38
O B. Ho: Po = 0
H;: Po >0
Apr-18
May-18
3.25
5.09
- 1.78
- 3.20
Jun-18
0.54
OC. Ho: B1 =0
H;: B, #0
Jul-18
Aug-18
Sept-18
Oct-18
Nov-18
Dec-18
Jan-19
Feb-19
2.88
2.69
1.29
3.58
7.41
O D. Ho: P1 =0
H;: P, > 0
- 4.83
- 2.38
1.48
- 4.40
- 0.86
- 6.12
2.37
- 4.27
- 3.77
Determine the P-value for this hypothesis test.
- 3.48
P-value =D (Round to three decimal places as needed.)
State the appropriate conclusion at the a = 0.10 level of significance. Choose the correct answer below.
Print
Done
O A. Reject H.. There is sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate of return of the company stock.
O B. Do not reject H,. There is sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate of return of the company stock.
OC. Do not reject Hp. There is not sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate of return of the company stock
O D. Reject H.. There is not sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate of return of the company stock.

(c) Assuming the residuals are normally distributed, construct a 90% confidence interval for the slope of the true least-squares regression line.
| (Round to four decimal places as needed.)
Upper bound: O (Round to four decimal places as needed.)
Lower bound:
(d) What is the mean rate of return for the company stock if the rate of return of the index is 3.45%?
The mean rate of return for the company stock if the rate of return of the index is 3.45% is %.
(Round to three decimal places as needed.)

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