,Example 17-11. (a) Show that if a most efficient estimator A and a less efficientestimator B with efficiency e tend to joint normality for large samples,B-A tends to zero correlation with A.(b) Show that the error in B may be regarded as composed (for large samples) of two partswhich are independent, the error in A and the error in (B -A).(c) Show further that V(A – B) = ( - 1)V(A).e

Answered: Image /qna-images/answer/e2952adb-eec9-4f75-a897-bdfb698051f1.jpg

Answered: Example 17-11. (a) Show that if a most…

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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Suppose IQ scores were obtained from randomly selected siblings. For 20 such pairs of people, the linear correlation coefficient is 0.867 and the equation of the regression line is y = 3.57 + 0.97x, where x represents the IQ score of the younger child. Also, the 20 x values have a mean of 96.75 and the 20 y values have a mean of 97.1. What is the best predicted IQ of the older child, given that the younger child has an IQ of 95? Use a significance level of 0.05. Click the icon to view the critical values of the Pearson correlation coefficient r. The best predicted IQ of the older child is (Round to two decimal places as needed.)
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A weight-loss program wants to test how well their program is working. The company selects a simple random sample of 51 individual that have been using their program for 15 months. For each individual person, the company records the individual's weight when they started the program 15 months ago as an x-value. The subject's current weight is recorded as a y-value. Therefore, a data point such as (205, 190) would be for a specific person and it would indicate that the individual started the program weighing 205 pounds and currently weighs 190 pounds. In other words, they lost 15 pounds. When the company performed a regression analysis, they found a correlation coefficient of r = 0.707. This clearly shows there is strong correlation, which got the company excited. However, when they showed their data to a statistics professor, the professor pointed out that correlation was not the right tool to show that their program was effective. Correlation will NOT show whether or not there is…
Suppose that you run a regression of Y, on X, with 110 observations and obtain an estimate for the slope. Your estimate for the standard error of ₁ is 1. You are considering two different hypothesis tests: The first is a one-sided test: Ho: B1-0, Ha: 31>0, a = .05 The second is a two-sided test: Ho: 31-0, Ha: B1 0,a = .05 (a) What values of , would lead you to reject the null hypothesis in the one-sided test? (b) What values of , would lead you to reject the null hypothesis in the one-sided test? (c) What values of would lead you to reject the mill hypothesis in the one-sided test, but not the two-sided test? (d) What values of 3 would lead you to reject the null hypothesis in the two-sided test, but not the one-sided test?
There may be an association between a country's birthrate and the life expectancy of its inhabitants. A report this past year, coming from a random sample of 20 countries, contained the following information: the least-squares regression equation relating the two variables number of births per one thousand people (denoted by x) and female life expectancy (denoted by y and measured in years) is y = 82.28 – 0.51 x, and the standard error of the slope of this least-squares regression line is approximately 0.35. Based on this information, test for a significant linear relationship between these two variables by doing a hypothesis test regarding the population slope B,. (Assume that the variable y follows a normal distribution for each value of x and that the other regression assumptions are satisfied.) Use the 0.10 level of significance, and perform a two-tailed test. Then complete the parts below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the…
11. In this same article on sleep duration and start time, researchers also considered whether school start time was related to obtaining an adequate amount of sleep. An adequate amountbof sleep was considered at least 8.5 hours of sleep, as recommended by the National Sleep Foundation. The authors used logistic regression models to associate the probability of adequate sleep to school start time. Here are some adapted logistic regression results from this study: In(odds of adequate sleep) = 6, + B,, where x1 = school start time, measured as the number of minutes after 7 AM that the school starts. For this model, B,-0.014, SE(B,)-0.005. - What Is the estimated odds ratlo of adequate sleep, and 95% CI, for students who start at 8:30 AM compared to those who start at 7:30 AM? a. 1.01 (1.00, 1.02) b. 1.52 (1.13, 2.05) C. 2.32 (1.27, 4.22) d. 4.05 (1.49, 11.02)
4, 12. How Call v. 13. Suppose that two raters (Rater A and Rater B) each assign pirysica attractiveness scO = not at all attractive to 10 = extremely attractive) to a set of seven facial photogranhe 21 %3D Pearson's r can be used as an index of interrater reliability or agreement on quantitative ratings. A correlation of +1 would indicate perfect rank-order agreement between rate while an r of 0 would indicate no agreement about judgments of relative attractiveness An r of .8 to .9 is considered desirable when reliability is assessed. For this example, Rater A's score is the X variable and Rater B's score is the Y variable. The ratings are as followe F follows: Photo Rater A Rater B 1 3. 5. 8. 6. 7. 8. 6. 4. 6. 10 6. 7. 5. 4. a. Compute the Pearson correlation between the Rater A and Rater B attractiveness ratings. What is the obtained r value? b. Is your obtained r statistically significant (using a =.05, two tailed)? Are the Rater A and Rater B scores "reliable"? Is there good or…
Show calculations or explanation for each question. a) Which of the following techniques is used to predict the value of one variable on thebasis of other variables?a. Correlation analysisb. Coefficient of correlationc. Covarianced. Regression analysis b) In the least squares regression line, y^=3-2x the predicted value of y equals:a. 1.0 when x = −1.0b. 2.0 when x = 1.0c. 2.0 when x = −1.0d. 1.0 when x = 1.0 c) In the simple linear regression model, the y-intercept represents the:a. change in y per unit change in x.b. change in x per unit change in y.c. value of y when x = 0.d. value of x when y = 0.
Example 3 : The tangent of the angle between two regression lines is 0.6 and if 1 =-0,, find the correlation coefficient between x and y. 2
3

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