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. Rate of Return Month Rates of return of theindex, x Rates of return of the company stock, y Apr-18 4.234.23 3.283.28 May-18 3.353.35 5.095.09 Jun-18 negative 1.78−1.78 0.540.54 Jul-18 negative 3.20−3.20 2.882.88 Aug-18 1.291.29 2.692.69 Sept-18 3.583.58 7.417.41 Oct-18 1.481.48 negative 4.83−4.83 Nov-18 negative 4.40−4.40 negative 2.38−2.38 Dec-18 negative 0.86−0.86 2.372.37 Jan-19 negative 6.12−6.12 negative 4.27−4.27 Feb-19 negative 3.48−3.48 negative 3.77−3.77 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 beta 0β0 and beta 1β1. The estimate of beta 0β0 is 1.23001.2300. (Round to four decimal places as needed.) The estimate of beta 1β1 is 0.76480.7648. (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 company stock, y, at the alphaαequals=0.10 level of significance. Choose the correct answer below. State the null and alternative hypotheses. A. Upper H 0H0: beta 0β0equals=0 Upper H 1H1: beta 0β0greater than>0 B. Upper H 0H0: beta 0β0equals=0 Upper H 1H1: beta 0β0not equals≠0 C. Upper H 0H0: beta 1β1equals=0 Upper H 1H1: beta 1β1not equals≠0 D. Upper H 0H0: beta 1β1equals=0 Upper H 1H1: beta 1β1greater than>0 Determine the P-value for this hypothesis test. P-valueequals= 0.0260.026 (Round to three decimal places as needed.) State the appropriate 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 linear relation exists between the rate of return of the index and the rate of return of the company stock. B. Do not reject Upper H 0H0. 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. Do not reject Upper H 0H0. 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. D. Reject Upper H 0H0. 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. (c) Assuming the residuals are normally distributed, construct a 90% confidence interval for the slope of the true least-squares regression line. Lower bound: 0.23760.2376 (Round to four decimal places as needed.) Upper bound: 1.29101.2910 (Round to four decimal places as needed.) (d) What is the mean rate of return for the company stock if the rate of return of the index is 3.153.15%? The mean rate of return for the company stock if the rate of return of the index is 3.153.15% is 3.6393.639%. (Round to three decimal places as needed.)

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. Rate of Return Month Rates of return of theindex, x Rates of return of the company stock, y Apr-18 4.234.23 3.283.28 May-18 3.353.35 5.095.09 Jun-18 negative 1.78−1.78 0.540.54 Jul-18 negative 3.20−3.20 2.882.88 Aug-18 1.291.29 2.692.69 Sept-18 3.583.58 7.417.41 Oct-18 1.481.48 negative 4.83−4.83 Nov-18 negative 4.40−4.40 negative 2.38−2.38 Dec-18 negative 0.86−0.86 2.372.37 Jan-19 negative 6.12−6.12 negative 4.27−4.27 Feb-19 negative 3.48−3.48 negative 3.77−3.77 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 beta 0β0 and beta 1β1. The estimate of beta 0β0 is 1.23001.2300. (Round to four decimal places as needed.) The estimate of beta 1β1 is 0.76480.7648. (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 company stock, y, at the alphaαequals=0.10 level of significance. Choose the correct answer below. State the null and alternative hypotheses. A. Upper H 0H0: beta 0β0equals=0 Upper H 1H1: beta 0β0greater than>0 B. Upper H 0H0: beta 0β0equals=0 Upper H 1H1: beta 0β0not equals≠0 C. Upper H 0H0: beta 1β1equals=0 Upper H 1H1: beta 1β1not equals≠0 D. Upper H 0H0: beta 1β1equals=0 Upper H 1H1: beta 1β1greater than>0 Determine the P-value for this hypothesis test. P-valueequals= 0.0260.026 (Round to three decimal places as needed.) State the appropriate 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 linear relation exists between the rate of return of the index and the rate of return of the company stock. B. Do not reject Upper H 0H0. 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. Do not reject Upper H 0H0. 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. D. Reject Upper H 0H0. 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. (c) Assuming the residuals are normally distributed, construct a 90% confidence interval for the slope of the true least-squares regression line. Lower bound: 0.23760.2376 (Round to four decimal places as needed.) Upper bound: 1.29101.2910 (Round to four decimal places as needed.) (d) What is the mean rate of return for the company stock if the rate of return of the index is 3.153.15%? The mean rate of return for the company stock if the rate of return of the index is 3.153.15% is 3.6393.639%. (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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Question

Rate of Return

Month	Rates of return of theindex, x	Rates of return of the company stock, y
Apr-18	4.234.23	3.283.28
May-18	3.353.35	5.095.09
Jun-18	negative 1.78−1.78	0.540.54
Jul-18	negative 3.20−3.20	2.882.88
Aug-18	1.291.29	2.692.69
Sept-18	3.583.58	7.417.41
Oct-18	1.481.48	negative 4.83−4.83
Nov-18	negative 4.40−4.40	negative 2.38−2.38
Dec-18	negative 0.86−0.86	2.372.37
Jan-19	negative 6.12−6.12	negative 4.27−4.27
Feb-19	negative 3.48−3.48	negative 3.77−3.77

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

beta 0β0

and

beta 1β1.

The estimate of

beta 0β0

1.23001.2300.

(Round to four decimal places as needed.)

The estimate of

beta 1β1

0.76480.7648.

(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 company stock, y, at the

alphaαequals=0.10

level of significance. Choose the correct answer below.

State the null and alternative hypotheses.

Upper H 0H0:

beta 0β0equals=0

Upper H 1H1:

beta 0β0greater than>0

Upper H 0H0:

beta 0β0equals=0

Upper H 1H1:

beta 0β0not equals≠0

Upper H 0H0:

beta 1β1equals=0

Upper H 1H1:

beta 1β1not equals≠0

Upper H 0H0:

beta 1β1equals=0

Upper H 1H1:

beta 1β1greater than>0

Determine the P-value for this hypothesis test.

P-valueequals=

0.0260.026

(Round to three decimal places as needed.)

State the appropriate conclusion at the

alphaαequals=0.10

level of significance. Choose the correct answer below.

Reject

Upper H 0H0.

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.

Do not reject

Upper H 0H0.

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.

Do not reject

Upper H 0H0.

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.

Reject

Upper H 0H0.

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.

(c) Assuming the residuals are normally distributed, construct a 90% confidence interval for the slope of the true least-squares regression line.

Lower bound:

0.23760.2376

(Round to four decimal places as needed.)

Upper bound:

1.29101.2910

(Round to four decimal places as needed.)

(d) What is the mean rate of return for the company stock if the rate of return of the index is

3.153.15%?

The mean rate of return for the company stock if the rate of return of the index is

3.153.15%

3.6393.639%.

(Round to three decimal places as needed.)

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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