B.13. Table B-6 gives data on the number of new business incorporations (Y) and the number of business failures (X) for theUnited States from 1984 to 1995. a. What is the average value of new business incorporations?And the variance? b. Whatis the average value of business failures? And the variance? c. What is the covariance between Y and X? And the correlationcoefficient? (X) + var (Y) sr= -0.8 (X+Y) 2X = 16, s2Y = 9Y = 3X2 + 2Y = ax + bY = X>4Y = 0.6X-4 Y = 3X+2 E(X) = 8 and var (X) = 4 E(XY) = a 4X=1 a 2 Y = 1 XIYi f(XI, YI) X = 20 NUMBER OF NEW BUSINESSINCORPORATIONS (Y) AND NUMBER OF BUSINESS FAILURES (X), UNITED STATES, 1984-1995 YEAR Y X1984 634,991 52,078 1985 664,235 57,253 1986 702, 738 61,616 1987 685,572 61, 111 1988 685,095 57,097 1989 676,565Source: Economic Report of the President, 2004, Table B-96, p. 395. TABLE B-6 d. Are the two variables independent? e. Ifthere is correlation between the two variables, does this mean that one variable causes the other variable? That is, do newincorporations cause business failures, or vice versa?

To address the problem, let's first identify the data provided and the questions that need to be…

Answered: B.13. Table B-6 gives data on the…

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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List two possible limitations of using a Pearson correlation coefficient.
2. The correlation between the price indices of animal feeding-stuffs and home-grown cats in a sample of 60 members is 0.68. Could the observed value have arisen: (a) from an uncorrelated population? (b) from a population in which true correlation was 0-8?
4.38 Statistics for Investing. A mutual funds company’s newsletter says “A well-diversified portfolio includes assets with low correlations.” The newsletter includes a table of correlations between the returns on various classes of investments. For example, the correlation between municipal bonds and large-cap stocks is 0.50, and the correlation between municipal bonds and small-cap stocks is 0.21. Rachel invests heavily in municipal bonds. She wants to diversify by adding an investment whose returns do not closely follow the returns on her bonds. Should she choose large-cap stocks or small-cap stocks for this purpose? Explain your answer. If Rachel wants an investment that tends to increase when the return on her bonds drops, what kind of correlation should she look for?
What is the Pearson's r correlation coefficient for a sample set of data with values (1,2), (2,3), (3,4), (4,5)?
why are correlations useful in econometrics?
Systematic variability occurs when: A. there are too many control variables B. there is a lot of variability in the data C. there is a design confound D. there are too many dependent variable
ps-5
A group of university researchers wanted to determine the relationship that exists between the number of hours spent by a student in social media in a day (X) and their grade weighted average (Y). Twelve randomly selected students produced the following findings: Number of GWA Hours 4.0 95 8.0 85 87 89 91 85 89 86 84 96 82 85 7.0 6.5 5.5 9.0 4.0 10.0 7.5 2.0 12.0 9.0
The accompanying table shows the earnings per share (in dollars) and the dividends per share (in dollars) for 6 companies in a recent year. Complete parts (a) through (d) below. Click here to view the data table. Click here to view the table of critical values for the Pearson correlation coefficient. (a) Display the data in a scatter plot. Choose the correct.graph below. OA. OB. В. Oc. OD. 3- 9- Q Q 2- 6- 6- 3- 3- 04 3. Eamings per share (S) Eamings per share ($) 0. Eamings per share (S) Eamings per share (S) (b) Calculate the sample correlation coefficient r. - X Data Table (Round to three decimal places as needed.) (c) Describe the type of correlation, if any, and interpret the correlation in the context of the data. Earnings per share, x Dividends per share, y O 1.36 1 There is V linear correlation. 4.3 0.59 3.56 8.27 1.74 2.47 Interpret the correlation. Choose the correct answer below. 1.19 0.67 1.6 2.82 O A. Increases in companies' eamings per share cause their dividends per share…
Example 3. Calculate Correlation Coefficient from the data given below by direct method i.e., without taking deviations of items from actual or assumed mean Roll No. of Students : Marks in Maths : Marks in Stat : 2 3 4. 48 35 17 23 47 45 20 40 25 45.
4.A corporation imposes different price increases on its product in eight different regions of the country and measures over the next year changes in sales volume. The results are shown in the accompanying table. Change in 6 5 4 7 7 10 8 Price (Percentage) Change in 5.2 7.3 7.4 4.6 5.3 5.0 -1.0 2.9 Sales (Percentage) a. Find correlation coefficient between change in price and change in sales and test it whether it is statistically significant at 0.05 significance level. b. Determine which variable is dependent variable and which variable is independent variable based on the original variables, estimate the regression model and interpret the model. c. Run hypothesis testing at 0.05 signi ance level whether the egression coefficient bị is statistically significant or not. d. Calculate R2 value and interpret the result e.Predict the dependent variable value when independent variable is 4.8 and interpret the result.
5.Stocks and Mutual Fund Ownership It has been found that 51.4% of U.S. households own stocks and mutual funds. A random sample of 300 heads of households indicated that 178 owned some type of stock. At what level of significance would you conclude that this was a significant difference? Use the P-value method. Assume the variable normally distributed. Use a graphing calculator. Find the P-value. At what level of significance is this a significant difference?

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