4. Let X, Y be two random variables. We want to investigate if there is a linearrelationship between them. If there is, we should be able to approximate Y witlha + bX for some constants a,b. To evaluate the fit of such approximation, wemeasure the error by considering the average squared distance between Y anda + bX, that is,expanding the RHSA small Emeans a good fit.(a) Determine the critical values of a, b by setting the partial derivatives(a, b)(b) With the critical values from parta), the minimum value of E(a, ó) (after lotsof cancellation) is (1-r2 y) Var(y), where ρxy s the correlation coefficientbetween X, Y. With this conclusion, determine the range of ρχ.y

Given X, Y are tow randon variables.E(a,b) = E (Y-(a+bX))2 = E(Y2 ) + a2 + b2 E(X2 ) - 2aE(Y)…

Answered: 4. Let X, Y be two random variables. We…

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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For 50 randomly selected speed dates, attractiveness ratings by males of their female date partners (x) are recorded along with the attractiveness ratings by females of their male date partners (y); the ratings range from 1 to 10. The 50 paired ratings yield x-6.4, y= 6.1, r= - 0.226, P-value = 0.115, and y = 7.81 - 0.269x. Find the best predicted value of y (attractiveness rating by female of male) for a date in which the attractiveness rating by the male of the female is x= 6. Use a 0.10 significance level. The best predicted value of y when x= 6 is (Round to one decimal place as needed.)
A random sample X1, X2, ..., Xn is obtained for a random variable X believed to be distributed as Beta(a, 7) (notice that B = 7 is known). Use the method of moments to determine the value of given 0.72.
For 50 randomly selected speed dates, attractiveness ratings by males of their female date partners (x) are recorded along with the attractiveness ratings by females of their male date partners (y); the ratings range from 1 to 10. The 50 paired ratings yield x= 6.4, y = 6.0, r= - 0.267, P-value = 0.061, and y= 7.90- 0.296x. Find the best predicted value of y (attractiveness rating by female of male) for a date in which the attractiveness rating by the male of the female is x= 4. Use a 0.01 significance level. The best predicted value of y when x= 4 is. (Round to one decimal place as needed.)
5. Suppose Y₁, Y2,..., Y are independent random variables whose density is for y0 for some > 0. (a) Show that the MLE for is f(y) = 30y²e-04³ n ÔMLE = ΣΤ (b) Use the R code to estimate the bias and the variance when n = 20 and 0 = 2.
Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 139 to 194 cm and weights of 39 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x= 167.63 cm, y = 81.47 kg, r=0.106, P-value = 0.294, and y = - 108 + 1.04x. Find the best predicted value of y (weight) given an adult male who is 172 cm tall. Use a 0.05 significance level. The best predicted value of y for an adult male who is 172 cm tall is kg. (Round to two decimal places as needed.)
For 50 randomly selected speed dates, attractiveness ratings by males of their female date partners (x) are recorded along with the attractiveness ratings by females of their male date partners (y); the ratings range from 1 to 10. The 50 paired ratings yield x = 6.4, y = 6.0, r=-0.233, P-value = 0.104, and ŷ= 7.88 -0.292x. Find the best predicted value of y (attractiveness rating by female of male) for a date in which the attractiveness rating by the male of the female is x = 4. Use a 0.01 significance level. The best predicted value of y when x = 4 is (Round to one decimal place as needed.)
Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 138 to 188 cm and weights of 40 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x = 167.61 cm, y = 81.52 kg, r=0.271, P-value=0.006, and y = -103 +1.18x. Find the best predicted value of ŷ (weight) given an adult male who is 155 cm tall. Use a 0.10 significance level. The best predicted value of y for an adult male who is 155 cm tall is (Round to two decimal places as needed.) kg.
The length (in mm) of a spring subjected to a force FNewtons is of the form L = a + BF+ ɛ, where ɛ is assumed normally distributed with mean 0, variance o2. Given the sample statisticsn=D13, E F;= 138, E L; = 577, SEL = -43, SEF= 1735, estimate the expected length of the spring when a force of 11.2 Newtons is applied. (Give your answer correct to 2 decimal places.) Answer: Ti Check 江一 prime viden Type here to search 19 hp ins prt fu f12 f8 f9 f10 f7 f5 f6 『米 " JOI JDI & 6 7 8 5 96 %24 3
Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 132 to 193 cm and weights of 39 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x = 167.59 cm, y = 81.52 kg, r= 0.416, P-value = 0.000, and y = - 102 + 1.13x. Find the best predicted value of y (weight) given an adult male who is 147 cm tall. Use a 0.05 significance level. The best predicted value of y for an adult male who is 147 cm tall is kg. (Round to two decimal places as needed.)
The quality characteristic of a product Y consists of three components X1, X2, and X3. The distributions of these components are normal with means 100, 2, 1 and variances 1, 1, 1 respectively. The specifications of the product are 90 ± 8. If Y= X1 + -7X2 + -9X3. Products that are below the lower specification limit are scrapped. Find the proportion of scrapped products = Ф(z).
Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 137 to 189 cm and weights of 37 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x = 167.50 cm, y =81.41 kg, r=0.232, P-value = 0.020, and y = - 109 + 1.17x. Find the best predicted value of y (weight) given an adult male who is 145 cm tall. Use a 0.01 significance level. The best predicted value of y for an adult male who is 145 cm tall is kg. (Round to two decimal places as needed.)
Heights (cm) and weights (kg) are measured for 100 randomly selected adult males, and range from heights of 137 to 192 cm and weights of 40 to 150 kg. Let the predictor variable x be the first variable given. The 100 paired measurements yield x = 167.80 cm, y = 81.45 kg, r=0.211, P-value = 0.035, and y = -103 +1.07x. Find the best predicted value of ŷ (weight) given an adult male who is 145 cm tall. Use a 0.01 significance level. The best predicted value of y for an adult male who is 145 cm tall is (Round to two decimal places as needed.) kg.

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